Question

An automobile is moving down a straight road and braked with a constant acceleration of -5 m/s2. If the initial velocity of the car is 35 m/s and the final velocity of the car is 15 m/s, calculate the displace

Answer 1

The velocity $v$ of an object moving with a constant acceleration at any moment of time $t$ is given by the following formula:

$$v = v_0+at$$

where $v_0 =35m/s$ is the initial velocity of the car and $a = -5m/s^2$ is its acceleration. If we set $v = 15m/s$, we can find the time that was taken to reach from $v_0$ to $v$:

$$t = \dfrac{v-v_0}{a} = \dfrac{15-35}{-5} = 4s$$

The displacement after this time is:

$$d = v_0t + \dfrac{at^2}{2}\\ d = 35\cdot 4 - \dfrac{5\cdot 4^2}{2} = 100m$$

Answer. 100 m.