Question

A car, A, travelling along a straight road at a constant 30 . −1 , passes point R at time = 0. Exactly 2 seconds later, a second car, B, passes point R with velocity 25 . −1 , moving in the same direction as car A. Car B accelerates at a constant 2 . −2 . find the time when the two cars are level.

Answer 1

This section assumes you have enough background in calculus to be familiar with

where C1 is a constant of integration. Since

\[\int \frac{d}{dt}v(t)dt=v(t)\]

, the velocity is given by

\[v(t)=\int a(t)dt+{C}_{1}.\]

Similarly, the time derivative of the position function is the velocity function,

\[\frac{d}{dt}x(t)=v(t).\]

Thus, we can use the same mathematical manipulations we just used and find

\[x(t)=\int v(t)dt+{C}_{2},\]

where C2 is a second constant of integration.