1. ## Velocity and acceleration..

A car accelerates to overtake a truck. Its initial speed is u, and in a time t after it starts to accelerate it covers a distance x, where x = ut + kt^2.

Use differentiation to show that its speed is then u + 2kt, and show that its acceleration is constant.

Then velocity, dx / dt = u + 2kt ... which is also the speed in this case.

But how to show that acceleration is constant?

2. Just as speed is the derivative of the postion function, so acceleration is the derivative of the speed function. What is the derivative of u+ 2kt with respect to t?