Question

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?

Answer 1

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