Car with constant power?

Question

The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 mph. At full power, the car can accelerate from zero to 32.0 mph in time 1.50 s. At full power, how long would it take for the car to accelerate from 0 to 64 mph? Neglect friction and air resistance.

Thanks for the help!

Answer 1

3s

.
use the following formula.

Vf = V1 + at

where Vf = final velocity, V1 original velocity & a = accelaration, t time.

solve for accelaration

32mph = 0mph + a(1.5s)

a = 32mph/1.5s

now re-use equation to solve for time required to accelarate to 64mph.

Vf = V1 + at

64mph = 0 + (32mph/1.5s)t
solving for t you get

3 seconds

Answer 2

Power is work over a period of time and work is the change in kinetic energy of the car. 32.0 mph is 46.9 ft/s.

KE is 1/2mv^2, so the total work done is 1099.8m and that's in 1.5s. Divide the two to get 733.2 as your constant value for power.
Now, going from 0 to 64mph (or 93.9 ft/s) is 4408.6m.

So, 4408.6/t = constant. So, 4408.6 over your constant of 733.2 will give you the time. It takes 6.01s for the car to accelerate to 64 mph.

Just to note, the two answers below mine are incorrect. They are interpreting your question as constant acceleration, but you said constant power. It takes more energy to go from 5 mph to 10 mph than from 0 mph to 5 mph if you ignore friction and this is why it takes so much longer to go from 0 to 64 than from 0 to 32.

Answer 3

Answer: 6.00s

Answer 4

If the power is the same, then it can accelerate to twice the speed in twice the time. Since 64 MPH is twice 32 MPH, it would be 3 seconds.

Answer 5

Chris S provided the correct way to solve the problem and also the correct solution. The other two are incorrect.

Answer 6

It is 6 seconds. That is the correct answer.