Calculating Acceleration of Car with Constant Power

[physics517]

Homework Statement

A car has an engine which delivers a constant power. It accelerates from rest at time t = 0, and at t = t0 its acceleration is a0. What is its acceleration at t = 2t0? Ignore energy loss due to friction.

the answer is a0 /sqrt(2)

Homework Equations

work = Fd cos theta

Power= work/time

The Attempt at a Solution

Ive haven't done many problems involving power so I think I am lacking something conceptually here. The problem states that at time t0, the acceleration is a0, so i assumed that there is a change in acceleration which led me to think jerk and derivatives.

 

[Filip Larsen]

Can you write up an expression for how much energy the engine has delivered as a function of time t? If there is no friction where does all this energy end up, and can you relate this (well-known) energy to the engine energy? If so, a few more steps should provide you with acceleration as a function of time.

If you don't know calculus (as I implied with the last hint above), you can instead use the general relationship between power on one side with that of force and velocity on the other, where force in this case is the inertial force from accelerating the car which thus can be replaced with mass and acceleration (Newtons 2nd law). Combining all these equation you should be able to solve for acceleration.

 

[gomunkul51]

Try:

Power = Energy(t)/t = const.

The power only affects the kinetic energy of the car, which is a function of velocity. you need to make it a function of time.

 

[physics517]

Ok so i initially tried this problem using calculus but I became confused. So then i tried the following

1/2 mv^2 / t = fd / t

= Fv
= mav

so then i solved for a which gave me a=v/ 2t

so where did i go wrong?

 

[gneill]

P = F*v
F = m*a
P*t = (1/2)m*v²

Go.

 

[gomunkul51]

You didn't found "Energy(t)" i.e. expression of energy as a function of time.

The energy is kinetic energy: K = 0.5mv²
you should know that v = at+v₀

P = const. = kineticEnergyAsFunctionOfTime/Time

now express t₀ in other terms you know e.g. P and a₀ and find the new acceleration.

Sit down and read again the question, what data you have? what do you need to find? plan the steps guided by your variables.