Question

A car started from rest and accelerates with 2.4 m/s2 for 8.8 seconds. It then travels with the constant velocity it has achieved for another 9.9 seconds. Then it finally slows to a stop with a constant acceleration of 3.4 m/s2. How far does the car travel after starting from rest?

Answer 1

367.616 m

Step-by-step explanation:

The distance it travels for the 1st segment is

`s_1 = a_1t_1^2/2 = 2.4*8.8^2/2 = 92.928 m`

The constant velocity that it achieves in the 2nd segment is

`v = a_1t_1 = 2.4 * 8.8 = 21.12 m/s`

The distance it travels in the 2nd segment is

`s_2 = vt_2 = 21.12 * 9.9 = 209.088 m`

The distance it travels in the last segment when coming from 21.12 m/s to rest (0 m/s) at the rate of -3.4 m/s2 is

`s_3 = (0^2 - v^2)/(2a_2) = (-21.12^2)/(2*(-3.4)) = 65.6 m`

The total distance is has traveled from rest is

92.928 + 209.088 + 65.6 = 367.616 m