The power is [tex]7.1\cdot 10^4 W[/tex]
Explanation:
First of all, we need to find the acceleration of the car, which is given by
[tex]a=\frac{v-u}{t}[/tex]
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,
[tex]a=\frac{26.8-0}{10.0}=2.68 m/s^2[/tex]
Now we can find the mass of the car by using Newton's second law:
[tex]F=ma[/tex]
where
F = 5300 N is the force applied
m is the mass
[tex]a=2.68 m/s^2[/tex] is the acceleration
Solving for m,
[tex]m=\frac{F}{a}=\frac{5300}{2.68}=1978 kg[/tex]
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:
[tex]W=K_f - K_i = \frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]
And substituting,
[tex]W=\frac{1}{2}(1978)(26.8)^2-0=7.10\cdot 10^5 J[/tex]
Finally, we can find the power output of the car:
[tex]P=\frac{W}{t}[/tex]
where
W is the work
t = 10.0 s is the time elapsed
Substituting,
[tex]P=\frac{7.1\cdot 10^5}{10.0}=7.1\cdot 10^4 W[/tex]
Learn more about power:
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