How does the constant power of an engine affect the acceleration of a car?

[raging11]

Homework Statement

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 30.0 mph in time 1.30s .

At full power, how long would it take for the car to accelerate from 0 to 60.0 mph ? Neglect friction and air resistance.

Homework Equations

No clue

The Attempt at a Solution

I assumed that since it takes 1.3s to go from 0-30, it would take 2.6 to got from 0-60, yet it was wrong and got this for a feedback. :
Think about how kinetic energy is related to velocity, and how power is related to energy.

 

[jdougherty]

The feedback you got should give you a clue as to what the relevant equations are. Do you know of some equations which relate kinetic energy to velocity and power to energy?

 

[raging11]

KE=1/2mv^2 and Power=??

 

[LowlyPion]

Welcome to PF.

Constant power is constant watts.

What is a watt? J/s

What is a joule?

well ... it's the units of ½mv² for one thing.

 

[bjd40@hotmail.com]

power = force(instantenuous) X speed (instantenuous)

 

[raging11]

Im still stumped! I have no clue how to transfer from knowing 1.3s at Full power to go from 0-60

 

[leah_91]

I would figure out the acceleration of the car first using the 0-30 in 1.3 sec. then use the known acceleration (since it would be constant at full power) to find out how long it would take the car to go 0-60 with that acceleration.

 

[LowlyPion]

Im still stumped! I have no clue how to transfer from knowing 1.3s at Full power to go from 0-60

Think of power then as something that is added at a constant rate. It's energy after all and as it collects it becomes kinetic energy of your car.

If it took one bucket of energy to get you to 1/2mv² then how many buckets of energy will it take to get you to 1/2m(2v)² ?

Since the buckets are added in this case at 1.3s per bucket - a constant rate -...