Question

Two cars cover the same distance in a straight line. Car a covers the distance at a constant velocity. Car b starts from rest and maintains a constant acceleration. Both cars cover a distance of 520 m in 223 s. Assume that they are moving in the x direction. Determine (a) the constant velocity of car a, (b) the final velocity of car b, and (c) the acceleration of car

b.

Answer 1

a) For the motion of car with uniform velocity we have ,
`s = ut+(1)/(2)at^2`, where s is the displacement, u is the initial velocity, t is the time taken a is the acceleration.

In this case s = 520 m, t = 223 seconds, a =0
`m/s^2`

Substituting

`520 = u*223\\ \\u = 2.33 m/s`

The constant velocity of car a = 2.33 m/s

b) We have
`s = ut+(1)/(2) at^2`

s = 520 m, t = 223 seconds, u =0 m/s

Substituting

`520 = 0*223+(1)/(2) *a*223^2\\ \\ a = 0.0209 m/s^2`

Now we have v = u+at, where v is the final velocity

Substituting

v = 0+0.0209*223 = 4.66 m/s

So final velocity of car b = 4.66 m/s

c) Acceleration = 0.0209
`m/s^2`