An electric vehicle starts from rest and accelerates at a rate of 2.1 m/s2 in a straight line until it reaches a speed of 25 m/s. The vehicle then slows at a constant rate of 1.2 m/s2 until it stops. (a) How much time elapses from start to stop

The vehicle takes 32.75 s from start to finish.

Explanation:

The vehicle trajectory has two stages, we gonna solve them separatly.

The first one where it is accelerating from 0 to 25 m/s, since the rate is constant at 2.1 m/s^2 we can find how much time it takes from this vehicle to reach it's final velocity. This is obtained by the following equation:

t = (V_final - V_initial) / rate

t = (25 - 0) / 2.1 = 11.91 s

The second one the vehicle is deaccelerating from 25 m/s to 0, since the rate is constant at 1.2 m/s^2 we can use the same equation, but now the rate is negative. So we have:

t = (V_final - V_initial) / rate

t = (0 - 25) / (-1.2) = 20.84 s

The total time it takes for it perform the whole trajectory is the sum of the time it takes to perform each part. So we have total time = 11.91 + 20.84 = 32.75 s.