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Question

# The position of a particle along x-axis at time t is given by x=1+tâˆ’t2. 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 mThe correct option is DGiven,Trajectory of motion of particle is x=1+t−t2. So, this is the parabolic equation. So, differentiate x with respect to time dxdt=0+1−2t0=1−2t ⇒t=12=0.5At t=0. , we have to check $\dfrac{d^2x}{dt^2}.Now, again differentiate$\dfrac{dx}{dt} with respect to td2xdt2=−2 Which is <0Hence, 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+0.5−0.25−1|+|1+2−4−1−0.5+0.25|=0.75+|−2−0.25|=0.75+2.25 =3m.

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