Question

A car traveling at 50 metre per seconds from rest covers a distance of 10km calculate the acceleration

Answer 1

Assuming the constant acceleration, the covered distance is given by:

$$d = \dfrac{at^2}{2}$$

where $d = 10\times10^3m$ is the distance, $a$ is the acceleration and $t$ is the time.

On the other hand, by definition, the acceleration is:

$$a = \dfrac{v - 0}{t} = \dfrac{v }{t}$$

where $v = 50m/s$ is the final velocity and stands for the intitial velocity (start from rest).

Substituting the expression for $a$ into the first equation and expressing $t$ , get:

$$d = \dfrac{vt^2}{2t} = \dfrac{vt}{2}\\ t = \dfrac{2d}{v}$$

Substituting the last equation into the expression for $a$, obtain:

$$a = \dfrac{v^2}{2d} = \dfrac{50^2}{2\cdot 10\cdot 10^3} = 0.125 m/s^2$$

Answer. 0.125 m/s^2.