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So, let's go straight to the point: a = v - u / t

Kinetic Energy: 1/2 mv

^{2}

Ok, I understand that a acceleration, a change in velocity, will change the Kinetic Energy since v is part of the Kinetic energy equation.

But acceleration is not simply a change in velocity. It is the rate, time is involved.

So, I don't understand how we can use Kinetic Energy to answer a question like this for example: Assuming that all the power of the motor is used to accelerate the cars, calculate how long they will take to reach their maximum speed.

For the question above though, we are given the power, is it correct to say therefore that:

Acceleration = Rate of change in Velocity, a change in velocity, is equal to a change in Kinetic Energy, which is equal to work done.

Thus, Power being: Work Done / t

We have the work done, which is equal to Kinetic Energy, a change in velocity but also, over time, which is acceleration.

I hope I made my doubt clear. If not, please tell me so I can rephrase.

Thanks in advance.