1 Motion along a straight line Relativeness of motion Activity: Observations from inside and outside of a moving bus. When you look outside a moving bus, do the trees and houses appear to move backwards? What about your fellow passengers, they do not seem to be moving at all, right? However a person outside the bus would say that the tree is stationary while the bus and all its passengers are moving. Both of you are describing the motion of the same objects but then why is there a difference between your observation and that of a person outside the bus? Which one of you is wrong? Distance and displacement Activity: How far away is your school from your house? How much distance do you have to travel to reach school? What would be the length of a straight line drawn between your house and the school? Would this also be the shortest distance that you would have to travel to get to school?
2 How much distance do you travel in one round trip to the school (go to the school and come back home)? How far away are you from your home after the round trip? Definition = length of the actual path taken to go from source to destination. = length of the straight line joining the source to the destination or in other words the length of the shortest path. Checkpoint Can the displacement of an object be greater than the distance travelled by that object? Suppose it was given that the person started by point A and walked in a straight line for 5 km. Can you find the end point of his/her journey? Sample Problem: Distance and displacement Rahul and Shreya start walking from their school. Rahul walks 2 km to the east while Shreya walks 1 km to the west and then turns back and walks another 1 km. What is the distance travelled by each one of them? Is Rahul s displacement the same as Shreya s displacement? Why is the displacement different?
3 Sample Problem: Distance and displacement Distance AB = 2 km due East Distance BC = 3 km due North Calculate the distance and displacement of a person who moves from A to C via B? Rate of motion Definition Speed: Velocity: Checkpoint When will the speed of an object be equal to its speed? Sample Problem: Speed and velocity The adjoining figure shows a Formula 1 racing track. A driver did 10 laps during a race. If the driver took 360 seconds to complete the laps, what is his speed and velocity in km/h? Radius of track (r) = Distance covered in one lap (s 1 ) = Number of laps (n) = Total distance covered (s) = Time taken (t) = Speed =? Velocity =?
4 Formula to be used: Definition Sample Problem: Average speed A car moves at a speed of 10 m/s for the first 5 seconds and then at a speed of 20 m/s for the next 15 seconds. Calculate the average speed and the average velocity of the car. First part of the journey Speed (s) = Time (t) = Second part of the journey Speed (s) = Time (t) = Average speed =? Average velocity =? Uniform motion Activity: Describing motion using distance-time graph Look at the graph on the right. What information does it provide to you? What would you call such a graph?
5 How much distance is covered every 10 seconds? Time interval Distance covered 0 10 seconds 11 20 seconds 21 30 seconds 31 40 seconds Activity: Describing motion using a speed-time graph Calculate the speed of the object at 10s, 20s, 30s and 40s from the graph below. Represent this information using a speed-time graph. Calculate the area under the line in the speed-time graph? Is this area equal to the distance covered by the object? Definition Uniform motion: Non-uniform motion:
6 Rate of change of velocity Definition Acceleration is defined as the rate of change of velocity. Activity: Describing motion using a velocity-time graph What does the graph of the right represent? Calculate the acceleration of the object? Is it constant? Initial velocity = Final velocity = What is the distance covered by the car in 30 seconds? Checkpoint Does the graph below represent an object moving with constant acceleration? Sample Problem: Interpreting velocity-time graphs Answer the following questions based on the adjoining figure. a. Which object has the maximum acceleration? b. Which object has no acceleration? c. How much distance is covered by object D in 20 seconds? d. Explain the motion represented by D. Given an example of such a motion in real life.
7 Equations of motion for an object moving with uniform velocity or uniform acceleration The first equation of motion (finding velocity of an object) Initial velocity = u Final velocity = v Time = t Acceleration = a Displacement = s Acceleration = Rate of change of velocity The second equation of motion (finding the displacement of an object) Initial velocity = u Final velocity = v Time = t Acceleration = a Displacement = s Displacement = Area under the line
8 The third equation (relationship between the displacement and velocity) Initial velocity = u Final velocity = v Time = t Acceleration = a Displacement = s Displacement = Area under the line Equations of motion:
9 Sample Problem: First equation of motion Colonel John P. Stapp set the world s speed record when he rode a rocket-propelled sled that moved down a track at 1020 km/hr. He and the sled were bought to a stop in 1.4 s. What acceleration did he experience? Initial velocity (u) = Final velocity (v) = Time taken (t) = Acceleration =? Sample Problem: Second equation of motion A motorcycle is moving at 30 m/s when the rider applies the brakes, giving the motorcycle a constant deceleration of 5 m/s 2 for 3 s. What is the distance covered by the motorcycle in the 3 s? Initial velocity (u) = Final velocity (v) = Acceleration (a) = Time taken (t) = Distance covered (s) =?
10 Sample Problem: Third equation of motion A jumbo jet must reach a speed of 360 km/h on the runway to take off. What is the least constant acceleration needed for takeoff from a 1.8 km runway? Initial speed (u) = Final speed (v) = Distance to be covered (s) = Acceleration (a) =?
11 Questions and Problems Vectors and Scalars 1. Most of the quantities used to describe motion can be categorized as either vectors or scalars. A vector is a quantity which is fully described by both magnitude and direction. A scalar is a quantity which is fully described by magnitude alone. Categorize the following quantities by placing them under one of the two column headings displacement, distance, speed, velocity and acceleration. Scalar Vector 2. A quantity which is ignorant of direction is called as quantity. Distance and Displacement 3. True or False: An object can be moving for 10 seconds and still have zero displacement. Explain why? 4. Suppose that you run along three different paths from location A to location B. Along which path(s) would your distance traveled be different than your displacement?. 5. A person starts at point A, walks along the bold path and finishes at B. Each square is 1 km along its edge. The person walks a distance of km. The displacement of the person is km. Speed and Velocity 6. A swimmer moves from location A to location B to location C to location D. Each leg of the back and forth motion (A B, B C and C D) takes 1 minute to complete; the total time is 3 minutes. Calculate the average speed (in m/min) and the average velocity (in m/min) during each of the three minutes.
12 Time Average Speed Average Velocity 0 1 min 1 2 min 2 3 min 7. On average, a blink lasts about 100 ms. How far does a fighter jet travel during a pilot s blink if the plane s average velocity is 3000 km/h.
13 8. Carl Lewis ran the 100 m dash in 10s, and Bill Rodgers ran the marathon (42 km) in 2 hr. and 20 min. What are their average speeds (in m/s)? If Lewis could have maintained his sprint speed during a marathon. How long would he take to finish the marathon?
14 9. A car travels on a straight road for 40 km at 30 km/hr. It then continues in the same direction for another 40 km at 60 km/hr. What is the average velocity of the car during this 80 km trip? (Assume that moves along a positive x direction). 10. In 1960, U.S. Air Force Captain Joseph Kittinger broke the records for the both the fastest and the longest sky dive... he fell an amazing 30 km! His average speed while falling was about 400 km/hour. How much time did the dive last?
15 11. Calculate the displacement of the person whose velocity-time graph is shown in the figure below. Uniform Acceleration 12. Answer the following questions based on the adjoining figure. a. Which object has the minimum acceleration? b. Which of the two has more acceleration A or B? c. How much distance is covered by object C in 10 seconds? 13. An object is accelerating if. (Select all that apply). a. with changing speed b. in a circle c. extremely fast d. with a constant velocity e. none of these 14. A car speeds from rest to a speed of 16 m/s in 4 s. Calculate the acceleration of the car. 15. Which of the following are correct for an object that has an acceleration of 10 m/s 2? a. The object will change its velocity by 10m/s in 1 s b. The object will move 10 m in 1 s c. The object will move 100 m in 10 s d. The object will have a velocity of 100 m/s after 10 s.
16 16. Describe the motion represented by the graphs below 17. Categorize the following motions as being either examples of + or - acceleration. a. A car moving in the + direction with increasing velocity b. A car moving in the + direction with brakes applied c. A ball thrown from the top of a building d. A car is moving in the - direction and slowing down Represent this graphically. Equations of motion 18. A motorcycle is moving at 30 m/s when the rider applies the brakes, giving the motorcycle a constant deceleration. During the 3 second interval immediately after the rider applies the brakes, the speed decreases to 15 m/s. What is the distance covered by the motorcycle in the 3 seconds?
17 19. An object has a constant acceleration of 4 m/s 2. At a certain instant its velocity is 12 m/s. What was its velocity 2.5 seconds earlier? Calculate the velocity of the object after another 2.5 seconds. 20. An airplane accelerates down a run-way at 3.20 m/s 2 for 30 s until is finally lifts off the ground. Determine the distance traveled before take-off.
18 21. Ram is driving his car at 25.0 m/s. He accelerates at 2.0 m/s 2 for 5 seconds. He then maintains a constant velocity for 10 more seconds. Determine the distance which Ram traveled during the entire 15 seconds. 22. Sapna is driving through town at 25.0 m/s and begins to accelerate at a constant rate of -1.0 m/s 2. Eventually she comes to a complete stop. Represent Sapna s accelerated motion by sketching a velocity-time graph. Use kinematic equations to calculate the distance which Sapna travels while decelerating. Then use the velocity-time graph to determine this distance.