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 20 m/s. The vehicle then slows at a constant rate of 1.0 m/s2 until it stops. (a) How much time elapses from start to stop? (b) How far does the vehicle travel from start to stop?

Verified Answer :

a. How much time elapses from start to stop
v = u + at
 20 = 0 + 2t1
 t1 = 10 sec

 
2nd phase:
v = u - at

0 = 20 - 1 x t2

t2 = 20 sec

 
total time = t1+t2 = 10 + 20 = 30 sec

b.
1st phase:

  s = ut + 1/2at^2

s1 = 0 + 1/2 x 2 x (10)^2

s1 = 100 m

2nd phase:


By s = ut - 1/2at^2

s2 = 20 x (20) - 1/2 x 1 x (20)^2

s2 = 200 m
  total distance(s) = s1+s2 = 100 + 200 = 300 m

hope this helps