Rectilinear Motion

1 Study the velocity-time graph of a car moving along a straight line and answer the following questions : 1. What is its velocity at 2, 4, 5, 6, 7 and 8 s ? 2. What is acceleration of the car at 2, 4.5 and 6.5 s ? 3. What is displacement in 5 and 8 s ? 4. How far is the car from the starting point after 8 s ? 5. What is the distance moved in 8 s ? 6. What is average velocity over 8 s ? 7. What is average speed over 8 s ? For solutions and answers check the next page but do so only after making an attempt to solve the questions on your own. Please leave feed back after going through the file. Thank you. Author : S.C.Benjamin 2 Solutions and Answers 1. The velocity of the car at 2 s – 2 m/s , 4 s – 6 m/s , 5 s – 0 , 6 s --2 m/s , 7 s --2 m/s , and 8 s -0 Note that that the velocity is positive till the end of 5 s which means that it was moving , say , in positive x-direction. After 5 s its velocity is negative which means the car starts moving in the opposite direction or the negative x-direction. It continues to move in negative direction till the end of 8 s when it stops. 2. The car has zero velocity at start ( zero second ) and 6 m/s at 3 s. Thus, acceleration or the rate of change of velocity is : 2 6 0 2 3 ms− − = The acceleration is uniform or constant from 0 to 3 s. At 2 s it is 2 2 ms− . The car has uniform or constant velocity between 3 and 4 s and therefore zero acceleration. The acceleration between 4 and 5 s : 2 0 6 6 1 ms− − = − . The acceleration at 4.5 s is 2 6ms− − . 3. Displacement in 5 s : 1 (5 1) 6 18 2 + × = m , Displacement between 5 and 8 s : 1 (3 1) ( 2) 4 2 + × − = − m Displacement in 8 s = 18 + (-4) = 14 m. 4. The car is 14 m from the starting point. 5. The distance moved in 8 s : 18 + 4 = 22 m 6. Average velocity over 8 s : 1 14 7 1.75 8 4 displacement ms time − = = = 7. Average speed : it is total distance moved divided by total time. 1 22 2.75 8 ms− =