Answer to Question #172301 in Physics for Kenan

Question

The car is moving at a speed of 7 m / s. At a certain point, the driver applies the brakes, after which the car moves another 1.5 m before stopping completely. Assuming the car is moving at a speed of 14 m / s, determine the path it would take after the driver starts braking. Assume that the braking forces are equal in both cases.

Answer 1

Let's first find the deceleration of the car:

$$v^2=v_0^2+2ad,$$ $$a=\dfrac{v^2-v_0^2}{2d}=\dfrac{0-(7\ \dfrac{m}{s})^2}{2\cdot1.5\ m}=-16.3\ \dfrac{m}{s^2}.$$

Finally, we can determine the path it would take after the driver starts braking:

$$d=\dfrac{0-(14\ \dfrac{m}{s})^2}{2\cdot(-16.3\ \dfrac{m}{s^2})}=6.0\ m.$$