Question

Make an order-of-magnitude estimate of the power a car engine contributes to speeding the car up to highway speed. In your solution, state the physical quantities you take as data and the values you measure or estimate for them. The mass of a vehicle is often given in the owner’s manual.

Short answer

The power a car engine contributes to speeding the car up to highway speed is 30 horsepower.

Step-by-step solution

Defining the kinetic energy formula

The Kinetic energy k is

$k=\frac{1}{2}m{v}^2$

where

$k=$ Kinetic energy transfer

$m=$Mass of body

$v=$ Speed of body.

Calculation for the kinetic energy and power

From step (1) the useful kinetic energy is

A $1300-kg$ car speeds up from rest to $55.0mi/h=24.6m/s$in$15.0s$. The output work of the engine is equal to its final kinetic energy,

$$\begin{gathered} k=\frac{1}{2}m{v}^2 \\ =\frac{1}{2}\left(1300kg\right){\left(24.5m/s\right)}^2 \\ =390kJ \end{gathered}$$

The power is

$$\begin{gathered} Power=\frac{Energy}{time} \\ =\frac{390000J}{15.0s} \\ \approx {10}^{4}W \end{gathered}$$

which is around 30 HP (horsepower).