The power is 5037 W
Explanation:
As a first step, we calculate the acceleration of the car, which is given by:
[tex]a=\frac{v-u}{t}[/tex]
where
v = 11.0 m/s is the final velocity
u = 7.50 m/s is the initial velocity
t = 9.30 s is the time interval
Substituting,
[tex]a=\frac{11.0-7.50}{9.30}=0.38 m/s^2[/tex]
Now we can find the force exerted on the object, which is given by
[tex]F=ma[/tex]
where
m = 1430 kg is the mass of the car
[tex]a=0.38 m/s^2[/tex] is the acceleration
Substituting,
[tex]F=(1430)(0.38)=543.4 N[/tex]
The distance covered by the car is given by the equation:
[tex]d=ut+\frac{1}{2}at^2 = (7.50)(9.30)+\frac{1}{2}(0.38)(9.30)^2=86.2 m[/tex]
So now we can find the work done by the force produced by the engine, which is:
[tex]W=Fd=(543.4)(86.2)=46,841 J[/tex]
And finally the power, which is the ratio between work done and time taken:
[tex]P=\frac{W}{t}=\frac{46,841}{9.30}=5037 W[/tex]
Learn more about power and work here:
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