Question

A car is moving with a velocity of 2 m/s and accelerates at 1.2 m/s^2, covering a distance of 45 m. How long did the car accelerate?

Answer 1

Let's first find the final velocity of the car:

$$v^2=v_0^2+2ad,$$ $$v=\sqrt{v_0^2+2ad},$$ $$v=\sqrt{(2\ \dfrac{m}{s})^2+2\times1.2\ \dfrac{m}{s^2}\times45\ m}=10.58\ \dfrac{m}{s}.$$

Finally, we can find the time that the car takes to accelerate:

$$v=v_0+at,$$ $$t=\dfrac{v-v_0}{a}=\dfrac{10.58\ \dfrac{m}{s}-2\ \dfrac{m}{s}}{1.2\ \dfrac{m}{s^2}}=7.15\ s.$$