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/s².

 

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/s².

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/s² × 80²s²) = 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: V² = V_o² + (2ad)

 

V² = (20m/s)² + (2 × 0.5m/s² × 120m)

V² = 400m²/s² + 120m²/s² = 520m²/s².

So, V = √520 = 22.8m/s.

 

In simple, at 80s the distance covered is 3200m whereas at 120m, the velocity is 22.8m/s. At 0m the velocity is 20m/s and at 3200m the velocity is 60m/s.