An older-model car accelerates from 0 to speed v in 9.0 s. A newer, more powerful sports car of the same mass accelerates from 0 to 3v in the same time period. Assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars. (Take Pnew and Pold as the powers of the new car and old car, respectively.)

The new car has 9 times the power of the old car

Explanation:

Given data

old car

Mass =m

Velocity =v

Time to attain the velocity t= 9secs

New car

Mass =m (same as old car)

Velocity =3v

Time to attain the velocity t= 9secs

We know that the kinetic energy expression is given as

KE=1/2mv²

KE for old car =1/2mv²J

KE for new car =1/2m(3v)²

=1/2m9v²J

Now the expression for power is

P= energy *time

Pold = 1/2mv²*9

4.5(mv²)Hp

Pnew = 1/2m*9v²*9

1/2m*81*v²

40.5(m*v²)Hp

Now comparing the powers of both cars

Pnew/Pold =40.5mv²/4.5mv²

Pnew/Pold = 9

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