Answer to Question #218814 in Physics for katiieee

Question

A car travelling at 15 m/s comes to rest in a distance of 14 m when the brakes are applied.

Calculate the deceleration of the car.

Answer 1

According to the work-energy theorem, the amount of work required to stop the car is equal to its initial kinetic energy:

$$W = \dfrac{mv^2}{2}$$

where $v = 15m/s$ and $m$ is the mass of the car.

On the other hand, the work is given as follows:

$$W = Fd$$

where $d = 14m$ and $F$ is the friction force that were acting on the car. By the second Newton's law:

$$F = ma$$

where $a$ is the decceleration of the car. Combining this all together, obtain:

$$mad = \dfrac{mv^2}{2}\\ a = \dfrac{v^2}{2d}$$

Thus, obtain:

$$a = \dfrac{15^2}{2\cdot 14} \approx 0.57m/s^2$$

Answer. 0.57 m/s^2.