Question

The displacement of a particle is given by x = (t – 2)² where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is ______.

Options

• 4 m

• 8 m

• 12 m

• 16 m

Answer 1

The displacement of a particle is given by x = (t – 2)² where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is 8 m.

Explanation:

Given, `x = (t - 2)^2`

Velocity, `v = (dx)/(dt) = d/(dt) (t - 2)^2 = 2(t - 2)`  m/s

Acceleration, `a = (dv)/(dt) = d/(dt) [2(t - 2)]`

= `2[1 - 0]`

= 2 m/s²

When t = 0; v = – 4 m/s

t = 2s; v = 0 m/s

t = 4s; v = 4 m/s

v-t graph is shown in the adjacent diagram

Distance travelled = Area of the graph

= Area OAC + Area ABD

= `(4 xx 2)/2 + 1/2 xx 2 xx 4`

= 8 m