A bus stop is situated 400 m ahead of a stationary bus. The bus starts from rest, increases its speed uniformly with an acceleration of 1 m s⁻² until it attains a speed of 10 m s⁻¹, travels with this speed for some time, and finally comes to rest at the stop with a uniform retardation of 2 m s⁻².
(i) Calculate the time taken by the bus to reach the speed of 10 m s⁻¹.
(ii) Determine the distances covered during (a) the acceleration phase and (b) the retardation phase.
(iii) Find the time for which the bus travels with constant speed.
(iv) Obtain the total time taken for the journey from the initial position to the bus stop.