Question

Starting initially at rest at t=0, a subway car accelerates to 29 m/s over a period of 6 seconds, and then begins to brake. Forty-eight (total) seconds after starting, it is moving at 12 m/s . What is its average acceleration in this 48-s interval?

Answer 1

First, let's find the acceleration for the 6 s-interval. Since it started at rest, the initial velocity is 0. Then, the acceleration would be 

a = (29 - 0)/6 = 4.833 m/s²

For the rest of the interval, the time would be 48 s - 6 s = 42 s. The initial velocity at this point is 29 m/s and the final velocity is at 12 m/s. So the acceleration is

a = (12 - 29)/42 = -0.405 m/s²

Finally, the average acceleration is
Average acceleration = (4.833 + ⁻0.405)/2 = 2.214 m/s²