### Velocity, Acceleration

Velocity is (rate of) change in speed with time whereas acceleration is (rate of) change in velocity with time. A bike is moving at a velocity of 20m/s. Its speed gradually increases and after 80s its velocity is 60m/s and assume thereafter it maintains constant velocity. Estimate the acceleration and the distance travelled within this 80s. Also estimate the velocity at 120m. Here unit for velocity is, m/s. So, unit for acceleration is, m/s 2 . Acceleration, a = (V – V o ) / dt dt = 80s V – Velocity after time dt = 60m/s. V o – Velocity before time dt = 20m/s. Hence, a = [(60 – 20)m/s] / 80s = 0.5m/s 2 . Distance travelled (d) in this 80s is estimated by the formulae, d = (V o dt) + (0.5 × a × (dt) 2 ) d = (20m/s × 80s) + (0.5 × 0.5m/s 2 × 80 2 s 2 ) = 3200 m So, distance travelled during the acceleration from 20m/s to 60m/s is 3200 m. The velocity, V at a given distance, d (120m) is expressed as: V 2 = V o 2 + (2ad) V 2