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Question

The position of a particle along x-axis at time t is given by x=1+tt2. the distance travelled by the particle on first 2 second is

A
1 m
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B
2 m
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C
2.5 m
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D
3 m
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Solution

The correct option is B 3 m

The correct option is D

Given,

Trajectory of motion of particle is x=1+tt2. So, this is the parabolic equation.

So, differentiate x with respect to time

dxdt=0+12t

0=12t

t=12=0.5


At t=0. , we have to check $\dfrac{d^2x}{dt^2}.

Now, again differentiate $\dfrac{dx}{dt} with respect to t
d2xdt2=2 Which is <0
Hence, at t=0.5, particle reaches maximum velocity and also chanhinf the nature of motion [ after t=0.5 , particle is retardating ]

So, total distance can be found by

S=|x(t=0.5)x(t=0)|+|x(t=2)x(t=0.5)|
=|1+0.50.251|+|1+2410.5+0.25|
=0.75+|20.25|
=0.75+2.25

=3m.


967629_1018250_ans_1b44825e81d6426ea920aad81e936a7d.PNG

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