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 canaccelerate from zero to 32.0 mph in time 1.50 s.

Answer 1

The question talks about delivering constant POWER to the wheels. Power is a measure of the change in energy with respect to time. You can work out how much power it is constantly delivering by calculating the kinetic energy at 32 m.p.h after 1.5s. No mass is given but the mass will be the same at double the velocity so we can leave that out and just work with the velocity squared. 32^2/1.5 =Power = 682.67

This is the constant power available at 64 m.p.h. and the equation can be rearranged to determine the time to reach 64 m.p.h

time = Change in energy/power

Because the mass is the same we can just work the kinetic energy from 64^2 =4096

Therefore time = 4096/682.67 = 6

Double the speed, quadruple the energy. Therefore the time should be 4 times the original as the change of energy is delivered at a constant rate.

Answer 2

First, find the acceleration that this engine can create, using the equation:

v_f = v_i + at ; where v_f is final velocity, v_i is initial velocity, a is acceleration, and t is time...

32.0 mph = 0 mph + a(0.000417 hours) ; (I converted the time rather than the speed because this would take more work)

a = 32.0 mph/ 0.000417 hours

a = 76,800 miles/hour²

Now plug this acceleration back into the original equation and solve for time.

64.0 mph = 0 mph + (76,800 miles/hour²)t

t = (64.0 mph)/(76,800 miles/hour²)

t = 0.000833 hours

t = 3 seconds

As you can see, this is double the time it takes the car to accelerate to 32.0 mph which makes sense because the new speed (64.0 mph) is double theoriginal. That would be the faster way to do it, but it's worth it to work it out in detail and understand it all :)

Answer 3

6 seconds.  

Answer 4

If youre here looking for this question but in 1 second instead of 1.5 the answer is 4