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.

AHow much time elapses from start to stop?
BHow far does the vehicle travel from start to stop?

Verified Answer :

A1st phase:
v= at,   t=v/a=\(\frac{20 m/s}{2m/s^{2} }\)=10s
2nd phase:
0 m/s= 20 m/s - a
t,  at= 20 m/s, t=\(\frac{20 m/s}{1m/s^{2} }\)=20s
Total time: t1+t2=10 s+20 s = 30 s
b)Formula:  s=v0
t+at²/2 or s=v0t-at²/2
1st phase:
s=0+\(\frac{2*10^{2} }{2}\)=100m
2nd phase:
s=20 m/s
20 s-\(\frac{1*20^{2} }{2}\)=200 m
Total distance traveled: s1+s2 = 100 m + 200 m = 300 m.