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) 1st phase:
v= a*t, t=v/a=
`(20 m/s)/(2m/s^(2) )`=10s
2nd phase:
0 m/s= 20 m/s - a*t, a*t= 20 m/s, t=
`(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=v0*t-at²/2
1st phase:
s=0+
`(2*10^(2) )/(2)`=100m
2nd phase:
s=20 m/s*20 s-
`(1*20^(2) )/(2)`=200 m
Total distance traveled: s1+s2 = 100 m + 200 m = 300 m.