Question

10. The displacement of a body along x-axis depends on the time as t+1. Then the velocity of a
body
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Answer 1

Given that,

The displacement of a body along the x axis depends on time as x = t + 1.

To find :-

The velocity of the body.

Acknowledgement :-

Displacement = velocity × time

⇒Velocity = displacement/time

Solution :-

Differentiating the displacement function with respect to time :

$\sf{\displaystyle{ v=\frac{dx}{dt} }}\\\\\sf{\displaystyle{\implies v=\frac{d(t+1)}{dt} }}\\\\\sf{\displaystyle{\implies v=\frac{d(t)+d(1)}{dt} }}\\\\\sf{\displaystyle{\implies v=\frac{d(t)}{dt} +\frac{d(1)}{d(t)} }}\\\\\sf{\displaystyle{\implies v=1+0 }}\\\\ \sf{(Differentiation\ of\ a\ constant\ is\ 0.)}\\\\\boxed{\sf{\displaystyle{\implies v=1}}}$

So we can say that, the body moves with a constant velocity.