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 28.0mph in time 1.30s .

Part ? 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 28.0mph in time 1.30s, how long would it take to go from zero to 56.0mph ? Express your answer numerically, in seconds.

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 28mph to 56mph, energy needed is 2^2 = 4 times of energy.

So, time needed is 4 times.

Time to reach 56mph = 5.20s

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 56mph = 2.6s

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