The velocity of a car at time, ts^-1, during the first 20 s of its journey, is given by v = kt + 0.03t^2, where k is a constant. When t = 20 the acceleration of the car is 1.3ms^-2, what is the value of k?

Our task is to find out the value of k, which we can determine from the equations for velocity or acceleration if we know 2 of the 3 variables in either equation. We are given the value of acceleration at t(20)=1.3ms^-1, so we should substitute these values into the equation for acceleration, which we can calculate by differentiating the velocity: a = k + 0.06t. This gives us 1.3 = k + 0.06(20) -> 1.3 = k + 1.2 -> 0.1 = k.