Motion
Content
Contents 1. Distance and Displacement 2. Speed and Velocity 3. Displacement-Time Graph 4. Acceleration 5. Velocity-Time Graph 6. Falling Objects Exam Topics At the end of this chapter you should be able to state what is meant by speed, velocity and acceleration recognise motion for which the acceleration is constant and calculate the accele ration recognise motion for which the acceleration is not constant plot and interpret a speed-time graph recognise from a) at rest b) moving with c) moving with d) moving with the shape of a speed-time graph when a body is constant speed constant acceleration an acceleration that is not constant
calculate the area under a speed-time graph to determine the distance travelled for motion with constant speed or constant acceleration show understanding that the acceleration of free fall for a body near the Earth is constant Concept Map (Highlight comment Wangks 17/12/2011 3:57:34 PM blank) April 2000 Motion - 1 Physics@Xinmin
1. Distance and Displacement Distance Definition: Displacement Definition: Example: Q. A car travels 8 km due East and makes a U-turn back and travels a further 5 km due West. What is the distance covered by the car and what is its displacement at the end of the journey? 8 km 5 km A. Distance covered = Displacement = We say that Distance is a scalar it has magnitude only Displacement is a vector it has magnitude and direction Do the following physical quantities have any direction associated with them? i.e. are they scalars or vectors? PHYSICAL QUANTITIES SCALARS OR VECTORS Length Mass Weight Electric Current Density (Highlight comment Wangks 17/12/2011 3:57:28 PM blank) April 2000 Motion - 2 Physics@Xinmin
2. Speed and Velocity Speed Definition: Equation: v= s= t= Note: This equation is for instantaneous speed (actual speed). <v> is the average speed. 1 km = 1000 m and 1 hour = 60 × 60 s (= 3600 s) Thus, 1 km/h = 1000/3600 m/s 1 km/h = 5/18 m/s 1 m/s = 18/5 km/h Example: A car covers a distance of 15 km in 30 minutes. Q. What is the car s average speed? Q. Does the above answer tell us anything about the maximum or minimum speed of the car? Q. The above answer seems slow for a car explain why it is probably correct. (Highlight comment Wangks 17/12/2011 3:57:23 PM blank) April 2000 Motion - 3 Physics@Xinmin
Questions: 1. An aeroplane travelling at a constant speed covers a distance of 2750 km in a period of 2 hours 30 minutes. What is the speed of the aeroplane? 2. You run a race in 25 seconds. If your average speed for the race was 8 m/s, w hat distance was the race? 3. A man walks a distance of 2 km in 40 minutes. Calculate his average speed in i) km/h ii) m/s 4. Convert the following speeds between m/s and km/h. i) 10 m/s ii) 80 km/h (the speed limit on the Singapore expressways.) 5. You walk a distance of 2 km at an average speed of 6 km/h. You then run for a further 10 minutes with an average speed of 12 km/h. What is your average velocity for the whole journey? (Highlight comment Wangks 17/12/2011 3:57:18 PM blank) April 2000 Motion - 4 Physics@Xinmin
Velocity Velocity is a vector form of speed. Definition: Equation: Write in words the equation for a) velocity b) Average velocity Example: A car drives 20 km in an eastward direction and then 15 km in a westward directi on. It takes 20 minutes to complete its journey. Calculate a) average speed for the journey b) the average velocity for the journey (Highlight comment Wangks 17/12/2011 3:57:12 PM blank) April 2000 Motion - 5 Physics@Xinmin
3. Displacement-Time Graph A graph can be a very useful way to show information about how an object moves. One type of graph we can use is the Displacement-Time Graph. Image a ball being rolled along the ground, the positions of the ball are shown after equal time intervals. We can measure the distance of the balls from the start point and plot this info rmation on a graph. TIME (S) DISPLACEMENT (CM) 1 2 3 4 5 Use a suitable scale to copy the information onto the displacement-time graph be low. Displacement ( cm) Time (s) You should now have a straight-line graph. Q. What type of motion will produce this type of graph? (Highlight comment Wangks 17/12/2011 3:57:06 PM blank) April 2000 Motion - 6 Physics@Xinmin
Look at the displacement-time graphs below to determine how the objects are moving. 1. Type of motion: 2. Type of motion: 3. Type of motion: 4. Type of motion: 5. Type of motion: 6. Type of motion: (Highlight comment Wangks 17/12/2011 3:57:00 PM blank) April 2000 Motion - 7 Physics@Xinmin
Gradient of a Displacement-Time Graph In general the instantaneous speed (instantaneous velocity) can be calculated fr om the gradient of the graph at a point. Example: What is the speed at t=6 s? Questions: Look at the displacement-time graph below and answer the questions. a) At which position(s) is the velocity zero? b) At which position is the velocity the greatest? c) At which position is it farthest from the reference point? (Highlight comment Wangks 17/12/2011 3:56:55 PM blank) April 2000 Motion - 8 Physics@Xinmin
4. Acceleration Acceleration Definition: Equation: a= u= v= t= Example: 1. A car starting from rest is accelerated to a velocity of 48 10 seconds. Calculate the acceleration of the car. 2. A sports car is travelling at a constant velocity of 10 m/s to a velocity of 55 m/s in 3 seconds. What is the acceleration 3. A car initially has a velocity of 58 m/s. After braking for velocity of 33 m/s. Calculate the acceleration of the car. (Highlight comment Wangks 17/12/2011 3:56:51 PM blank) April 2000 Motion - 9 Physics@Xinmin m/s in a time of before accelerating of the car? 10 seconds it has a
Deceleration When an object changes its velocity (or speed) to become slower we can state thi s in several ways; we can say that the object; a) is ______________________, b) is ______________________ or c) has a _________________ _________________. Example: A train slows down from 60 m/s to rest in one minute. Calculate the retardation of the train. Uniform Acceleration Acceleration is said to be uniform if it remains constant over a period of time. Example: a) The velocity of a car increases from rest to 9 m/s in the first 3 s and then it increases from 9 - 27 m/s over the next 6 seconds. Is the acceleration of the ca r uniform? b) A car starts travelling from rest and undergoes constant acceleration for 10 seconds. If it is travelling at 6 m/s after 3 seconds what will be its final velocity? (Highlight comment Wangks 17/12/2011 3:56:47 PM blank) April 2000 Motion - 10 Physics@Xinmin
April 2000 Motion - 11 Physics@Xinmin 5. Velocity-Time Graph In a similar manner to the Displacement-Time (s-t) Graph the Velocity-Time (v-t) Graph can be used to find out a lot about the motion of an object. Note: Many things will be similar to the s-t graph, but not the same. If you are going to get confused forget the s-t graph. This is MUCH more IMPORTANT!! You sit in a car and record the velocity from the speedometer as the car pulls a way from some traffic lights. You obtain the data shown below. TIME (S) VELOCITY (M/S) 0 0 2 15 4 30 6 40 8 45 10 45 Plot this data on the graph below. Draw a smooth line through the points and we have a velocity-time graph of the motion of the car. 2 4 6 8 10 12 14 16 5 10 15 20 25 30 35 140 45 0 Time (s) Velocity (m/s)
Common Shapes of Velocity-Time Graphs The following six v-t graphs show the basic shapes that you will encounter. 1. At Rest (not moving) 2. Constant Velocity 3. Constant acceleration 4. Constant deceleration 5. Decreasing acceleration 6. Increasing acceleration (Highlight comment Wangks 17/12/2011 3:56:37 PM blank) April 2000 Motion - 12 Physics@Xinmin
Examples: 1. Look at the following velocity-time graph showing the velocity of an MRT train travelling between two stations. 35 B A C D 0 10 20 30 40 50 60 70 80 90 100110120130 Time(s) Velocity ( m Velocity ( m 30 25 20 15 10 5 0 AB BC CD
2. The following v-t graph shows the velocity of a car over a period of 12 seconds. Describe the motion of the car. 45 40 0 1 2 3 4 5 67 8 910 11 12 13 Time(s) 35 30 25 20 15 10 5 0 (Highlight comment Wangks 17/12/2011 3:56:31 PM
blank) April 2000 Motion - 13 Physics@Xinmin
A velocity-time graph can be used to find many things. Instantaneous velocity, Acceleration, and Distance travelled. Instantaneous Velocity from the V-T Graph Look at the graph on the left. 50 45 We can easily calculate the m 0123456 Time(s) 40 35 30 25 20 15 10 5 0 find the velocity at any instant. E.g. at t = 2, v = at t = 0.5, v = These are the instantaneous velocities at those times. Velocity ( Acceleration from the V-T Graph From the shape of the graph we know that the object is 45 undergoing constant 40 acceleration. 35
m 012345 Time(s) Velocity ( 30 25 20 15 10 5 0 What is the initial velocity? u = What is the velocity after 4 s? v = Acceleration can be calculated using v-u a = t (Highlight comment Wangks 17/12/2011 3:56:26 PM blank) April 2000 Motion - 14 Physics@Xinmin
Distance from the V-T Graph Q. If a car moves at 20 m/s for 5 seconds how far has it travelled? A. Distance = Velocity × Time = × = Alternatively we could have seen this from the v-t graph. 1. Shade the area under the graph. 2. Calculate the area you have shaded. Velocity (m/s) 25 20 15 10 5 0 012345 Time (s) Notes: You should see the area under the graph is equal to the distance covered. This is actually true for any v-t graph. Q. Can the equation "Distance = Speed × Time" be used on all occasions? A. No. This can only be used when the _______________ is _______________. Summary The velocity-time graph can be used to find: Instantaneous velocity Acceleration - from the gradient of the line Distance travelled - from the area underneath the graph (Highlight comment Wangks 17/12/2011 3:56:19 PM blank) April 2000 Motion - 15 Physics@Xinmin
Examples: 1. What distance does the car cover as it moves according to the v-t graph shown below? 25 Velocity (m/s) 20 15 10 5 0 0 5 101520253035 Time (s) 2. The graph below shows the motion of an MRT train as it passes from Yio Chu Kang to Ang Mo Kio to Bishan. 35 Velocity (m/s) 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 Time (s) a) How far did the MRT train travel in the first 20 seconds of its journey? b) How far is it from Ang Mo Kio to Bishan? (Highlight comment Wangks 17/12/2011 3:56:01 PM blank) April 2000 Motion 16 Physics@Xinmin
6. Falling Objects Q. Why do objects fall? A. Sir Isaac Newton Free-Fall Q. Drop a small object and a large object together. Which one will reach the floor the fastest? Q. What does this tell us about how objects fall? A feather and a hammer falling together will follow the same pattern. Both fall at the same rate. (Highlight comment Wangks 17/12/2011 3:55:56 PM blank) April 2000 Motion - 17 Physics@Xinmin
Use the information on the previous diagram to complete the following v-t graph for an object in free-fall near to the Earth. Velocity ( m 40 30 20 10 0 01234 Time(s) Q1. What does the shape of your graph tell you about the motion of the objects? Q2. In what ways, if any, would the same experiment be different if it had been carried out on the surface of the moon? Q3. What is the true value for the acceleration due to gravity near Earth? Problem with this theory: Q. But what if you had dropped a feather would it really fall at the same rate as a coin? A. Probably not. Why does the paper behave like this and why does a feather fall at the same rate as a coin in a vacuum? (Highlight comment Wangks 17/12/2011 3:55:48 PM blank) April 2000 Motion - 18 Physics@Xinmin
Air-Resistance Air resistance is the answer Walking through water is hard because it offers resistance to our motion. Air behaves in a similar manner to water and produces air resistance. This can b e felt when running very fast, when putting a hand through an open car window or in the form of wind blowing onto us. Air resistance depends on several factors: 1. 2. 3. 4. Terminal Velocity The following v-t graph shows the motion of a falling object. Describe how it moves from the start of its fall: (Highlight comment Wangks 17/12/2011 3:55:10 PM blank) April 2000 Motion - 19 Physics@Xinmin
Example 1: The following v-t graph shows the motion of a man as he parachutes out of an aeroplane. Q1. At which point on the graph does his parachute open? Q2. What is his terminal velocity without a parachute? Q3. What is his terminal velocity with a parachute? Draw the velocity-time graph for a stone thrown vertically into the air with a v elocity Q4. A heavier man also parachutes. Will his terminal velocity be identical to the lighter man? Explain. Example 2: of 20 m/s. Assume that the acceleration due to gravity is 10 m/s². 20 10 0 -10 -20 0 1 2 3 4 Time(s) Velocity ( m
(Highlight comment Wangks 17/12/2011 3:53:51 PM blank) (Highlight comment Wangks 17/12/2011 3:55:29 PM blank) April 2000 Motion - 20 Physics@Xinmin (Highlight comment Wangks 17/12/2011 3:53:31 PM blank)
calculate the area under a speed-time graph to determine the distance travelled for motion with constant speed or constant acceleration show understanding that the acceleration of free fall for a body near the Earth is constant Concept Map (Highlight comment Wangks 17/12/2011 3:57:34 PM blank) April 2000 Motion - 1 Physics@Xinmin
1. Distance and Displacement Distance Definition: Displacement Definition: Example: Q. A car travels 8 km due East and makes a U-turn back and travels a further 5 km due West. What is the distance covered by the car and what is its displacement at the end of the journey? 8 km 5 km A. Distance covered = Displacement = We say that Distance is a scalar it has magnitude only Displacement is a vector it has magnitude and direction Do the following physical quantities have any direction associated with them? i.e. are they scalars or vectors? PHYSICAL QUANTITIES SCALARS OR VECTORS Length Mass Weight Electric Current Density (Highlight comment Wangks 17/12/2011 3:57:28 PM blank) April 2000 Motion - 2 Physics@Xinmin
2. Speed and Velocity Speed Definition: Equation: v= s= t= Note: This equation is for instantaneous speed (actual speed). <v> is the average speed. 1 km = 1000 m and 1 hour = 60 × 60 s (= 3600 s) Thus, 1 km/h = 1000/3600 m/s 1 km/h = 5/18 m/s 1 m/s = 18/5 km/h Example: A car covers a distance of 15 km in 30 minutes. Q. What is the car s average speed? Q. Does the above answer tell us anything about the maximum or minimum speed of the car? Q. The above answer seems slow for a car explain why it is probably correct. (Highlight comment Wangks 17/12/2011 3:57:23 PM blank) April 2000 Motion - 3 Physics@Xinmin
Questions: 1. An aeroplane travelling at a constant speed covers a distance of 2750 km in a period of 2 hours 30 minutes. What is the speed of the aeroplane? 2. You run a race in 25 seconds. If your average speed for the race was 8 m/s, w hat distance was the race? 3. A man walks a distance of 2 km in 40 minutes. Calculate his average speed in i) km/h ii) m/s 4. Convert the following speeds between m/s and km/h. i) 10 m/s ii) 80 km/h (the speed limit on the Singapore expressways.) 5. You walk a distance of 2 km at an average speed of 6 km/h. You then run for a further 10 minutes with an average speed of 12 km/h. What is your average velocity for the whole journey? (Highlight comment Wangks 17/12/2011 3:57:18 PM blank) April 2000 Motion - 4 Physics@Xinmin
Velocity Velocity is a vector form of speed. Definition: Equation: Write in words the equation for a) velocity b) Average velocity Example: A car drives 20 km in an eastward direction and then 15 km in a westward directi on. It takes 20 minutes to complete its journey. Calculate a) average speed for the journey b) the average velocity for the journey (Highlight comment Wangks 17/12/2011 3:57:12 PM blank) April 2000 Motion - 5 Physics@Xinmin
3. Displacement-Time Graph A graph can be a very useful way to show information about how an object moves. One type of graph we can use is the Displacement-Time Graph. Image a ball being rolled along the ground, the positions of the ball are shown after equal time intervals. We can measure the distance of the balls from the start point and plot this info rmation on a graph. TIME (S) DISPLACEMENT (CM) 1 2 3 4 5 Use a suitable scale to copy the information onto the displacement-time graph be low. Displacement ( cm) Time (s) You should now have a straight-line graph. Q. What type of motion will produce this type of graph? (Highlight comment Wangks 17/12/2011 3:57:06 PM blank) April 2000 Motion - 6 Physics@Xinmin
Look at the displacement-time graphs below to determine how the objects are moving. 1. Type of motion: 2. Type of motion: 3. Type of motion: 4. Type of motion: 5. Type of motion: 6. Type of motion: (Highlight comment Wangks 17/12/2011 3:57:00 PM blank) April 2000 Motion - 7 Physics@Xinmin
Gradient of a Displacement-Time Graph In general the instantaneous speed (instantaneous velocity) can be calculated fr om the gradient of the graph at a point. Example: What is the speed at t=6 s? Questions: Look at the displacement-time graph below and answer the questions. a) At which position(s) is the velocity zero? b) At which position is the velocity the greatest? c) At which position is it farthest from the reference point? (Highlight comment Wangks 17/12/2011 3:56:55 PM blank) April 2000 Motion - 8 Physics@Xinmin
4. Acceleration Acceleration Definition: Equation: a= u= v= t= Example: 1. A car starting from rest is accelerated to a velocity of 48 10 seconds. Calculate the acceleration of the car. 2. A sports car is travelling at a constant velocity of 10 m/s to a velocity of 55 m/s in 3 seconds. What is the acceleration 3. A car initially has a velocity of 58 m/s. After braking for velocity of 33 m/s. Calculate the acceleration of the car. (Highlight comment Wangks 17/12/2011 3:56:51 PM blank) April 2000 Motion - 9 Physics@Xinmin m/s in a time of before accelerating of the car? 10 seconds it has a
Deceleration When an object changes its velocity (or speed) to become slower we can state thi s in several ways; we can say that the object; a) is ______________________, b) is ______________________ or c) has a _________________ _________________. Example: A train slows down from 60 m/s to rest in one minute. Calculate the retardation of the train. Uniform Acceleration Acceleration is said to be uniform if it remains constant over a period of time. Example: a) The velocity of a car increases from rest to 9 m/s in the first 3 s and then it increases from 9 - 27 m/s over the next 6 seconds. Is the acceleration of the ca r uniform? b) A car starts travelling from rest and undergoes constant acceleration for 10 seconds. If it is travelling at 6 m/s after 3 seconds what will be its final velocity? (Highlight comment Wangks 17/12/2011 3:56:47 PM blank) April 2000 Motion - 10 Physics@Xinmin
April 2000 Motion - 11 Physics@Xinmin 5. Velocity-Time Graph In a similar manner to the Displacement-Time (s-t) Graph the Velocity-Time (v-t) Graph can be used to find out a lot about the motion of an object. Note: Many things will be similar to the s-t graph, but not the same. If you are going to get confused forget the s-t graph. This is MUCH more IMPORTANT!! You sit in a car and record the velocity from the speedometer as the car pulls a way from some traffic lights. You obtain the data shown below. TIME (S) VELOCITY (M/S) 0 0 2 15 4 30 6 40 8 45 10 45 Plot this data on the graph below. Draw a smooth line through the points and we have a velocity-time graph of the motion of the car. 2 4 6 8 10 12 14 16 5 10 15 20 25 30 35 140 45 0 Time (s) Velocity (m/s)
Common Shapes of Velocity-Time Graphs The following six v-t graphs show the basic shapes that you will encounter. 1. At Rest (not moving) 2. Constant Velocity 3. Constant acceleration 4. Constant deceleration 5. Decreasing acceleration 6. Increasing acceleration (Highlight comment Wangks 17/12/2011 3:56:37 PM blank) April 2000 Motion - 12 Physics@Xinmin
Examples: 1. Look at the following velocity-time graph showing the velocity of an MRT train travelling between two stations. 35 B A C D 0 10 20 30 40 50 60 70 80 90 100110120130 Time(s) Velocity ( m Velocity ( m 30 25 20 15 10 5 0 AB BC CD
2. The following v-t graph shows the velocity of a car over a period of 12 seconds. Describe the motion of the car. 45 40 0 1 2 3 4 5 67 8 910 11 12 13 Time(s) 35 30 25 20 15 10 5 0 (Highlight comment Wangks 17/12/2011 3:56:31 PM
blank) April 2000 Motion - 13 Physics@Xinmin
A velocity-time graph can be used to find many things. Instantaneous velocity, Acceleration, and Distance travelled. Instantaneous Velocity from the V-T Graph Look at the graph on the left. 50 45 We can easily calculate the m 0123456 Time(s) 40 35 30 25 20 15 10 5 0 find the velocity at any instant. E.g. at t = 2, v = at t = 0.5, v = These are the instantaneous velocities at those times. Velocity ( Acceleration from the V-T Graph From the shape of the graph we know that the object is 45 undergoing constant 40 acceleration. 35
m 012345 Time(s) Velocity ( 30 25 20 15 10 5 0 What is the initial velocity? u = What is the velocity after 4 s? v = Acceleration can be calculated using v-u a = t (Highlight comment Wangks 17/12/2011 3:56:26 PM blank) April 2000 Motion - 14 Physics@Xinmin
Distance from the V-T Graph Q. If a car moves at 20 m/s for 5 seconds how far has it travelled? A. Distance = Velocity × Time = × = Alternatively we could have seen this from the v-t graph. 1. Shade the area under the graph. 2. Calculate the area you have shaded. Velocity (m/s) 25 20 15 10 5 0 012345 Time (s) Notes: You should see the area under the graph is equal to the distance covered. This is actually true for any v-t graph. Q. Can the equation "Distance = Speed × Time" be used on all occasions? A. No. This can only be used when the _______________ is _______________. Summary The velocity-time graph can be used to find: Instantaneous velocity Acceleration - from the gradient of the line Distance travelled - from the area underneath the graph (Highlight comment Wangks 17/12/2011 3:56:19 PM blank) April 2000 Motion - 15 Physics@Xinmin
Examples: 1. What distance does the car cover as it moves according to the v-t graph shown below? 25 Velocity (m/s) 20 15 10 5 0 0 5 101520253035 Time (s) 2. The graph below shows the motion of an MRT train as it passes from Yio Chu Kang to Ang Mo Kio to Bishan. 35 Velocity (m/s) 30 25 20 15 10 5 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 Time (s) a) How far did the MRT train travel in the first 20 seconds of its journey? b) How far is it from Ang Mo Kio to Bishan? (Highlight comment Wangks 17/12/2011 3:56:01 PM blank) April 2000 Motion 16 Physics@Xinmin
6. Falling Objects Q. Why do objects fall? A. Sir Isaac Newton Free-Fall Q. Drop a small object and a large object together. Which one will reach the floor the fastest? Q. What does this tell us about how objects fall? A feather and a hammer falling together will follow the same pattern. Both fall at the same rate. (Highlight comment Wangks 17/12/2011 3:55:56 PM blank) April 2000 Motion - 17 Physics@Xinmin
Use the information on the previous diagram to complete the following v-t graph for an object in free-fall near to the Earth. Velocity ( m 40 30 20 10 0 01234 Time(s) Q1. What does the shape of your graph tell you about the motion of the objects? Q2. In what ways, if any, would the same experiment be different if it had been carried out on the surface of the moon? Q3. What is the true value for the acceleration due to gravity near Earth? Problem with this theory: Q. But what if you had dropped a feather would it really fall at the same rate as a coin? A. Probably not. Why does the paper behave like this and why does a feather fall at the same rate as a coin in a vacuum? (Highlight comment Wangks 17/12/2011 3:55:48 PM blank) April 2000 Motion - 18 Physics@Xinmin
Air-Resistance Air resistance is the answer Walking through water is hard because it offers resistance to our motion. Air behaves in a similar manner to water and produces air resistance. This can b e felt when running very fast, when putting a hand through an open car window or in the form of wind blowing onto us. Air resistance depends on several factors: 1. 2. 3. 4. Terminal Velocity The following v-t graph shows the motion of a falling object. Describe how it moves from the start of its fall: (Highlight comment Wangks 17/12/2011 3:55:10 PM blank) April 2000 Motion - 19 Physics@Xinmin
Example 1: The following v-t graph shows the motion of a man as he parachutes out of an aeroplane. Q1. At which point on the graph does his parachute open? Q2. What is his terminal velocity without a parachute? Q3. What is his terminal velocity with a parachute? Draw the velocity-time graph for a stone thrown vertically into the air with a v elocity Q4. A heavier man also parachutes. Will his terminal velocity be identical to the lighter man? Explain. Example 2: of 20 m/s. Assume that the acceleration due to gravity is 10 m/s². 20 10 0 -10 -20 0 1 2 3 4 Time(s) Velocity ( m
(Highlight comment Wangks 17/12/2011 3:53:51 PM blank) (Highlight comment Wangks 17/12/2011 3:55:29 PM blank) April 2000 Motion - 20 Physics@Xinmin (Highlight comment Wangks 17/12/2011 3:53:31 PM blank)
