Does Constant Power Result in Constant Acceleration for a Car?

[mnandlall]

Homework Statement

Car, mass 1000kg, accelerates from rest in straight line using constant mechanical power of 60kW.
What is speed and acceleration after 5s.

Homework Equations

W = Kf - Ki
P= dE/dt

The Attempt at a Solution

I've already worked out that the speed will be 24.5m/s. What I'm really wondering is if a constant mechanical power results in a constant acceleration. Any help would be appreciated. Thanks.

 

[mnandlall]

I attempted to do the following:

F = ma, but F is provided by the motor. Therefore, P = Fv
60 000W = 24.5 x F
F = 2450 N

2450N = 1000kg x a
a = 2.45m/s^2

Does this seem like a reasonable approach?

 

[ogb p]

I would like to clarify that power, work, and speed are all related but distinct concepts in physics. Power is the rate at which work is done or energy is transferred, while work is the energy transferred when a force acts over a distance. Speed, on the other hand, is the rate at which an object changes its position over time.

To answer the question at hand, we can use the equation P = dE/dt, where P is power, dE is change in energy, and dt is change in time. Since we are given the power (60kW) and the mass of the car (1000kg), we can calculate the change in energy using the formula dE = P*dt. In this case, dE = 60kW*5s = 300kJ.

Now, we can use the equation W = Kf - Ki, where W is work, Kf is final kinetic energy, and Ki is initial kinetic energy. Since the car starts from rest, Ki = 0. Therefore, W = Kf - 0 = Kf. We know that work is equal to the change in energy (W = dE), so we can substitute 300kJ for W. This gives us the equation 300kJ = Kf, which means that the final kinetic energy of the car after 5 seconds is 300kJ.

To find the speed and acceleration, we can use the equations for kinetic energy and acceleration: Kf = 1/2mv^2 and a = (vf-vi)/t, where m is mass, v is velocity, and t is time. Substituting in the values we know, we get 300kJ = 1/2*1000kg*v^2 and a = (v-0)/5s.

Solving for v, we get v = √(300kJ*2/1000kg) = 24.49m/s, which is the speed after 5 seconds. To find the acceleration, we can substitute this value for v in the acceleration equation, giving us a = (24.49m/s - 0m/s)/5s = 4.898m/s^2. Therefore, the acceleration after 5 seconds is 4.898m/s^2.

In conclusion, a constant mechanical power of 60kW does not necessarily result in a constant acceleration