## Related questions with answers

A car of mass $m$ accelerates from rest along a level straight track, not at a constant acceleration but with constant engine power, $P$. Assume that air resistance is negligible. b) A second car starts from rest alongside the first car on the same track, but maintains a constant acceleration. Which car takes the initial lead? Does the other car overtake it? If yes, write a formula for the distance from the starting point at which this happens.

Solution

VerifiedIn this part of the problem, we have a second car starting from rest at the same time as the first car (see part **a)**), but maintaining a constant acceleration. It's velocity as a function of time is given by the well-known formula,

$\begin{equation} v_2(t)=at \end{equation}$

whereas for a non-constant acceleration, we obtained

$\begin{equation} v_1(t)=\sqrt{\dfrac{2P}{m}\ t} \end{equation}$

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