Question

A car, initially at rest, accelerates at 9 m/s2 for a total of 5.1 s. How far did it go in this time?

Answer 1

If a particle moves descibing a uniformly accelerated rectilinear motion, then, the distance that the particle travels Δx is related to the acceleration of the particle a, its initial speed v_0 and the time that it has traveled t, through the following equation:

`\Delta x=v_0t+(1)/(2)at^2`

Since the car is initially at rest, then v_0=0:

`\begin{gathered} \Delta x=0\cdot t+(1)/(2)at^2 \\ \Rightarrow\Delta x=(1)/(2)at^2 \end{gathered}`

Replace a=9m/s^2 and t=5.1s to find how far did the car travel during that time:

`\Delta x=(1)/(2)(9(m)/(s^2))(5.1s)^2=117.045m\approx117m`

Therefore, the car traveled a distance of 117 meters.