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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
Solution
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
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