Asports car starts from rest at an intersection and accelerates toward the east on a straight road at 8.0 m/s2. just as the sports car starts to move, a bus traveling east at a constant 18 m/s on the same straight road passes the sports car. when the sports car catches up with and passes the bus, (a) how much time has elapsed and (b) how far has the sports car traveled?

a)  t = 4.5 s , b)    x = 81 m

Explanation:

a) For this problem we will use kinematic relationships

For the car

        x = v₀ t + ½ a₁ t²

Since the car kicks from rest, the initial speed is zero

         x = ½ a₁ t²

For the bus

        v₂ = x / t

       x = v₂ t

At the point where they are located it has the same position, so we can match the equation

       ½ a₁1 t² = v₂ t

       ½ a₁ t = v₂

        t = 2 v₂ / a₁

Let's calculate

       t = 2 18 /8.0

       t = 4.5 s

b) to find the position

        x = v₂ t

        x = 18   4.5

        x = 81 m

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