Question

A car is moving at 60km/h when it begins to slow down with a deceleration of 1.5m/s^2. How long does it take to travel 70m as it slows down

Answer 1

Let's first find the final velocity:

$$v=\sqrt{v_0^2+2as}$$ $$v=\sqrt{(16.67\ \dfrac{m}{s})^2+2\cdot(-1.5\ \dfrac{m}{s^2})\cdot70\ m}=8.24\ \dfrac{m}{s}.$$

Finally, we can find the time that the car takes to travel 70 m as it slows down:

$$d=\dfrac{1}{2}(v+v_0)t,$$ $$t=\dfrac{2d}{v+v_0}=\dfrac{2\cdot70\ m}{8.24\ \dfrac{m}{s}+16.67\ \dfrac{m}{s}}=5.62\ s.$$