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  • The displacement of a particle is given by x = (t-2)^{2} where x is in metres and t is seconds. The distance covered by the particle in first 4 seconds is a) 4 m b) 8 m c) 12 m d) 16 m

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

a) 4 m

b) 8 m

c) 12 m

d) 16 m

Answers (1)

The answer is the option (b) 8m

Explanation:  It is given that, x = (t-2)^{2}

Now, we know that,

V=\frac{dx}{dt}

   = 2 (t - 2) m/s

&

a=\frac{d^{2}x}{dt^{2}}

       = 2 (1 - 0)

        =2\; ms^{-2}

Now,

v_{0} = 2(0-2) = -4 m/s \; \; \; \; \; \; \;............ (at\; t = 0)

v_{2} = 2(2-2) = 0\; m/s \; \; \; \; \; \; \;............ (at\; t = 2)

v_{4} = 2(4-2) = 4\; m/s \; \; \; \; \; \; \;............ (at\; t = 4)

Now, the distance is equal to the area between the time-axis graph and the (v-t) graph,

=\frac{1}{2}(2.4)+\frac{1}{2}(2.4)

 =8\; m

Hence, option (b).

Posted by

infoexpert22

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