Question

A certain car's drive-train produces a force of 5300 N as it accelerates from 0

Answer 1

The power is $7.1\cdot 10^4 W$

Explanation:

First of all, we need to find the acceleration of the car, which is given by

$a=\frac{v-u}{t}$

where

v = 60 mph = 26.8 m/s is the final velocity

u = 0 is the initial velocity

t = 10.0 s is the time

Substituting,

$a=\frac{26.8-0}{10.0}=2.68 m/s^2$

Now we can find the mass of the car by using Newton's second law:

$F=ma$

where

F = 5300 N is the force applied

m is the mass

$a=2.68 m/s^2$ is the acceleration

Solving for m,

$m=\frac{F}{a}=\frac{5300}{2.68}=1978 kg$

Now we can use the work-energy theorem, which states that the work done is equal to the change in kinetic energy of the car, to find the work:

$W=K_f - K_i = \frac{1}{2}mv^2-\frac{1}{2}mu^2$

And substituting,

$W=\frac{1}{2}(1978)(26.8)^2-0=7.10\cdot 10^5 J$

Finally, we can find the power output of the car:

$P=\frac{W}{t}$

where

W is the work

t = 10.0 s is the time elapsed

Substituting,

$P=\frac{7.1\cdot 10^5}{10.0}=7.1\cdot 10^4 W$

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