## 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. c) You are in a drag race, on a straight level track, with an opponent whose car maintains a constant acceleration of $12.0 \mathrm{~m} / \mathrm{s}^2$. Both cars have identical masses of 1000 . kg. The cars start together from rest. Air resistance is assumed to be negligible. Calculate the minimum power your engine needs for you to win the race, assuming the power output is constant and the distance to the finish line is $0.250 \mathrm{mi}$.

Solution

VerifiedGiven the following data

$\begin{aligned} a&=12.0\ \mathrm{\dfrac{m}{s^2}}\\ m&=1000.\ \mathrm{kg}\\ x&=0.250\ \mathrm{mi}\left(\dfrac{1609\ \mathrm{m}}{1\ \mathrm{mi}}\right)\\ &=402\ \mathrm{m} \end{aligned}$

our objective is to calculate the minimum power $P_{min}$ required to win the race.

To do so, we'll make use of the result obtained in part **b)**,

$\begin{equation} x=\dfrac{512P^2}{81m^2a^3} \end{equation}$

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