Question

The velocity time graph of a particle is given by

(i) Calculate distance and displacement of particle from given v - t graph.

(ii) Specify the time for which particle undergone acceleration, retardation and moves with constant velocity.

(iii) Calculate acceleration, retardation from given v - t graph.

(iv) Draw acceleration – time graph of given v - t graph.

Answer 1

(i) Distance = area of ∆AOB + area of trapezium BCDE = 12 + 28 = 40 m 

Displacement = area of ∆OAB – area if trapezium BCDE = 12 – 28 s = −16 m.

(ii) Time for acceleration − 0 ≤ t ≤ 4 

Time for retardation – 4 ≤ t ≤ 8

Time for constant velocity – 8 ≤ t ≤ 12

(iii) Acceleration = \(\frac{v}{t}=\frac{4}{4}=1\,m/s^2\)

Retardation = \(\frac{-4}{2}=-2\,m/s^2\)

(iv)