Question

The light turns green and a stationary racing car accelerates at 7.815 m/s/s. How much time does it take the car to reach a velocity of 37.0 m/s?

Answer 1

Assuming the acceleration stays constant, we have

`a=(v-v_0)/(t-t_0)`

where
`v` is the velocity of the car at time
`t`,
`v_0=0` is the starting velocity, and
`t_0=0` is the starting time. So

`a=\frac vt\iff7.815\,(\mathrm m)/(\mathrm s^2)=\frac{37.0\,(\mathrm m)/(\mathrm s)}t\implies t=(37.0\,(\mathrm m)/(\mathrm s))/(7.815\,(\mathrm m)/(\mathrm s^2))`

`\implies t\approx4.73\mathrm s`