A train is travelling at 50m/s. How long does it take the train to reach 60m/s if it accelerates at a constant rate of 0.5m/s^2? How many kilometres does it travel in this time?

The initial velocity, u, is 50 ms^-1 The final velocity, v, is 60 ms^-1 The acceleration, a, is 0.5ms^-2 The question is asking us to find the time, t. The equation of motion linking u, v, a, and t is v = u + at First we must rearrange the equation to make t the subject: t = (v-u)/a then we can substitute in the values. t = (60-50)/0.5 = 20s Now to find the displacement, s, during this time we can use s = ut + 0.5at² s = 5020 + 0.50.5*20² = 1,100m = 1.1km