An electric vehicle starts from rest and accelerates at a rate of 2.0 m/s2 in a straight line until it reaches a speed of 21 m/s. The vehicle then slows at a constant rate of 1.1 m/s2 until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle move from start to stop?

total time = 29.59 sec

total distance = 310.70 m

Explanation:

given data

accelerates at a rate = 2.0 m/s²

speed = 21 m/s

slows at a constant rate = 1.1 m/s²

solution

first we take  equation of motion

v = u + at        1

21 = 0 + 2 × t

t = 10.5 sec

now in case of deceleration again we take here

0 = 21 - 1.1 × t

t = 19.09 sec

so that total time is

total time = 10.5 + 19.09

total time = 29.59 sec

and

in case of acceleration

v² = u² + 2as           2

21² = 0 + 2 × 2 × s

s = 110.25 m

and when it is in case of deceleration we take here

0 = 21² - 2 × 1.1 × s

s = 200.45 m

so that here total distance is

total distance = 110.25  + 200.45

total distance = 310.70 m