Question

A 1100 kg car traveling at 27 m/s starts to decelerate and comes to a complete stop after
578 m. What is the average braking force acting on the car?

Answer 1

Answer on Question#40908 – Physics – Mechanics

A 1100 kg car traveling at 27 m/s starts to decelerate and comes to a complete stop after 578 m. What is the average braking force acting on the car?

Solution:

$$\begin{array}{l} m = 1100 \, \text{kg} - \text{mass of the car}; \\ v = 27 \frac{m}{s} - \text{initial speed of the car}; \\ d = 578 \, \text{m} - \text{traveled distance}; \end{array}$$

Loss of KE by car = work done by friction force:

$$W = \Delta E_k$$

Work done by friction force (minus sign - because the force is directed against the movement)

$$W = -F \cdot d$$ $$\Delta E_k = E_{k2} - E_{k1} = 0 - \frac{m v^2}{2} = - \frac{m v^2}{2}$$ $$(3) \text{ and } (2) \text{ in } (1):$$ $$- F \cdot d = - \frac{m v^2}{2}$$ $$F = \frac{m v^2}{2 d} = \frac{1100 \, \text{kg} \cdot \left(27 \frac{m}{s}\right)^2}{2 \cdot 578 \, \text{m}} = 694 \, \text{N}$$

Answer: average braking force acting on the car is equal to 694 N.