Answer to Question #169747 in Physics for Festus

Question

A car moving with a speed of 50 km/hr, can be stopped by brakes after at least 6m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is ___

Answer 1

Let's first find the deceleration of the car:

$$v^2=v_0^2+2ad,$$ $$a=\dfrac{v^2-v_0^2}{2d},$$ $$a=\dfrac{0-(50\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{1\ h}{3600\ s})^2}{2\cdot6\ m}=-16.07\ \dfrac{m}{s^2}.$$

Finally, we can find the minimum stopping distance if the same car is moving at a speed of 100 km/hr:

$$v^2=v_0^2+2ad,$$ $$d=\dfrac{v^2-v_0^2}{2a},$$ $$d=\dfrac{0-(100\ \dfrac{km}{h}\cdot\dfrac{1000\ m}{1\ km}\cdot\dfrac{1\ h}{3600\ s})^2}{2\cdot(-16.07\ \dfrac{m}{s^2})}=24\ m.$$