How Do You Calculate the Instantaneous Power of a Car Engine?

[404]

Car with mass of 1500kg, accelerates from 0 to 18 uniformly in 12 sec. Air drag is 400 N. Find the inst. Power output of engine at t = 12s. just before car stops accelerating...

Well I found the average power to be 23850 w, but how would you get the instantaneous?

 

[courtrigrad]

$$P = \lim_{\Delta T\rightarrow 0} \frac{\Delta W}{\Delta t} = \frac{dW}{dt}$$

I think $$P = F\bullet v$$ for instantaneous power.

 

[quicknote]

To calculate the instantaneous power at t=12s, we can use the formula P = Fv, where P is power, F is force, and v is velocity. In this case, the force acting on the car is the net force, which is the force of the engine minus the force of air drag. The force of the engine can be calculated using Newton's second law, F=ma, where m is the mass of the car and a is the acceleration. Plugging in the given values, we get F = 1500kg * 18m/s^2 = 27000N. So the net force at t=12s is 27000N - 400N = 26600N.

Next, we need to find the velocity of the car at t=12s. We can use the formula v = u + at, where u is the initial velocity (which is 0 in this case), a is the acceleration, and t is time. Plugging in the given values, we get v = 0 + 18m/s^2 * 12s = 216m/s.

Now we can calculate the instantaneous power at t=12s by multiplying the force and velocity: P = 26600N * 216m/s = 5745600w. Therefore, the instantaneous power output of the engine at t=12s is 5745600w, just before the car stops accelerating.