Power Needed to Accelerate 700kg Car from Rest

[johnnyb]

Hey guys any help on this question would be much appreciated

A 700kg car accelerates from rest under constant power at t = 0. At t = 9s it is 117.7m from its starting position and its acceleration is then 1.09m/s2. Find the power, expended by the car's engine, neglecting frictional losses.

 

[whozum]

Power = Work / Time
Work = Force x Distance
Force = Mass x Acceleration

Power = Mass x Acceleration x Distance / Time

 

[johnnyb]

I thought of that, but below that it says

Hint: Start with the relationship between Power and Force, rearrange differentials to intergrate

This just confused me, and I thought maybe it wasn't that simple as what you posted above

 

[whozum]

All the integration will lead to the answer I gave you above.

But in that case:

$$dW = P dt$$

$$dW = F dx$$

$$P dt = F dx$$

Integrating both sides:

$$\int { P dt } = \int { F dx }$$

$$Pt = Fx$$

$$P = \frac{Fx}{t}$$

Thats as differential as I can get.

 

[johnnyb]

Ok thanks very much for your help