Answer to Question #142268 in Physics for Michael

Question

A car is traveling with a velocity of 14 m/s when the driver accelerates it at a rate of 2.3m/s 2 for 8
seconds. can you explain me step by step how to do it.

Answer 1

Let's find the velocity and distance travelled by the car in $t = 8s$. By definition, the acceleration is:

$$a = \dfrac{v_f - v_i}{t}$$

where $v_i = 14m/s$ is car's initial speed and $v_f$ is car's final speed after time $t$. Expressing the final speed, obtain:

$$v_f = v_i + at = 14m/s + 2.3m/s^2\times 8s = 32.4m/s$$

The distance travelled by the car is:

$$d = v_it + \dfrac{at^2}{2} = 14m/s\times 8s + \dfrac{2.3m/s^2\times (8s)^2}{2} = 112m + 73.6m = 185.6m$$

Answer. Distance 185.6m, speed 32.4m/s.