Question

A car starts at a speed of 30 meters per second and travels at a uniform acceleration of 10 seconds and achieves a speed of 60 meters per second. How far did the car travel?

Answer 1

The distance travelled under the uniform acceleration $a$ is:

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

where $v_i = 30m/s$ is the initial speed, and $t = 10s$ is the time.

By definition, acceleration is:

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

where $v_f = 60m/s$. Substituting $a$ into the first equation, obtain:

$$d = v_it + \dfrac12t(v_f - v_i) = \dfrac12t(v_f+v_i)\\ d = \dfrac12\cdot 10\cdot (60+30) = 450m$$

Answer. 450 m.