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?
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?