Question

An electric vehicle starts from rest and accelerates at a rate of 1.9 m/s2 in a straight line until it reaches a speed of 22 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? (b) How far does the vehicle move from start to stop?

Answer 1

(a) Consider, t1 = acceletaion time, s1 = distance travelled during this time

t2 = stopping time, s2 = distance travelled during this time

use the expression -

v = u + a*t

=> 22 = 0 + 1.9*t1

=> t1 = 22 / 1.9 = 11.58 s

for the stopping journey -

0 = 22 - 1.2*t2

=> t2 = 22/ 1.2 = 18.33 s

So, the total time elapsed from start to stop = 11.58 + 18.33 = 29.91 s

(b) distance travelled -

s = u*t + (1/2)*a*t^2

=> s1 = 0 + 0.5*1.9*11.58^2 = 127.4 m

and s2 = 22*18.33 - 0.5*1.2*18.33^2 = 403.26 - 201.59 = 201.67 m

So, the total distance travelled by the car = s1 + s2 = 127.4 + 201.67 = 329.07 m