The engine in an imaginary sports car can provide constant power to the wheels o

Question

The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At full power, the car can accelerate from zero to 32.0mph in time 1.10s .

A)

At full power, how long would it take for the car to accelerate from 0 to 64.0mph ? Neglect friction and air resistance. =4.40s

Part B

A more realistic car would cause the wheels to spin in a manner that would result in the ground pushing it forward with a constant force (in contrast to the constant power in Part A). If such a sports car went from zero to 32.0mph in time 1.10s , how long would it take to go from zero to 64.0mph ?

am not sure how to do part B

Explanation / Answer

With constant power, the car is gaining energy in a constant rate.
Kinetic energy is 1/2 m v^2
So, as speed double from 32mph to 64mph, energy needed is 2^2 = 4 times of energy.
So, time needed is 4 times.
Time to reach 64mph = 4.40s

Now with constant force, since F=ma, so acceleration, a, is constant.
v = u + at => final speed is linear to time.
It will take twice time long to reach twice the final speed.
Time to reach 64mph = 2.20s

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