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 , $s = ut+\frac{1}{2}at^2$, 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 $s = ut+\frac{1}{2} at^2$

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

Substituting

      $520 = 0*223+\frac{1}{2} *a*223^2\\ \\ a = 0.0209 m/s^2$

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 $m/s^2$