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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 displacement of a particle is given by x=(t−2)2x = (t - 2)^{2}where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is

A

4 m

B

8 m

C

12 m

D

16 m

Answer

8 m

Explanation

Solution

Given: x =(t−2)2= (t - 2)^{2}

At t=0,x=x0=(0−2)2=4mt = 0,x = x_{0} = (0 - 2)^{2} = 4m

t=1s,x=x1=(1−2)2=1mt = 1s,x = x_{1} = (1 - 2)_{2} = 1m

t=2s,x=x2=(3−2)2=0mt = 2s,x = x_{2} = (3 - 2)^{2} = 0m

t=3s,x=x3=(3−2)2=1mt = 3s,x = x_{3} = (3 - 2)^{2} = 1m

t=4s,x=x4=(4−2)2=4t = 4s,x = x_{4} = (4 - 2)^{2} = 4

The distance covered by the particle in IstI^{st} seconds is D1=x0=x1=3mD_{1} = x_{0} = x_{1} = 3m

The distance covered by the particle in IIndII^{nd}second is D2=x1−x2=1mD_{2} = x_{1} - x_{2} = 1m

Similarly, D3=1m,D4=3mD_{3} = 1m,D_{4} = 3m

The distance covered by the particle in first 4 seconds is D=D1+D2+D3+D4D = D_{1} + D_{2} + D_{3} + D_{4}

= 3 m + 1m + 1m + 3m = 8