Answer to Question #298332 in Mechanics | Relativity for MishaTA

Question

A car of mass 350 Kg is travelling at 30 m/s when it starts to slow down, 100 m from a junction. At first, it slows just using the air resistance of 200 N then, at a distance of s m from the junction, it slows using brakes, providing a force of 2000 N as well as the air resistance. Find the distance from the junction at which the brakes must be applied if the car is to stop at the junction.

Answer 1

Explanations & Calculations

• Assuming there is no friction from ground we cam consider energy conservation from point to point.
• From the start (100 m) to the end point.
• If it comes to rest it should be due to the effect of friction forces that act on it.
• So all the kinetic energy it had at the beginning should be expended working against those forces.
• Therefore, kinetic energy is equal to the total work done by the external forces.

$\qquad\qquad \begin{aligned} \small \frac{1}{2}mv^2&=\small 200(100-s)+2200(s)\\ \small 0.5(350)(30)^2&=\small 20000+2000s\\ \small s&\approx\small 68.8\,m \end{aligned}$