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

$a=\dfrac{v-v_0}{t-t_0}$

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

$a=\dfrac vt\iff7.815\,\dfrac{\mathrm m}{\mathrm s^2}=\dfrac{37.0\,\frac{\mathrm m}{\mathrm s}}t\implies t=\dfrac{37.0\,\frac{\mathrm m}{\mathrm s}}{7.815\,\frac{\mathrm m}{\mathrm s^2}}$

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