Help on Physics kinematic problems please?

Question

1. Car 1 moves eastward with a constant speed of 20 m/s. Car 2, at rest on the side of the road, accelerates at 2 m/s squared to the east at precisely the instant Car 1 is beside it. How long does it take for Car 2 to catch up to Car 1?

 

2. Car 1 moves to the east with a constant speed of 20 m/s. Car 2 moves to the west with a constant speed of 30 m/s. How far from the start of Car 1 do the cars meet?

Answer 1

(1)

 

From the initial position of car 2, car 1 travels a distance

 

d = vt,

 

and car 2 travels the same distance distance, but given by

 

d = (1/2)at²

 

v = 20 m/s

a = 2 m/s²

 

(1/2)at² = vt

 

t = 2v/a = 2(20)/2 s = 20 s

 

(b)

 

To answer this question, we need to know how far apart the cars were at the beginning.