Question

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

Answer 1

As per the questions, the displacement function is given as :

x = t + 1

To find:

Velocity function of the body

Concept:

Displacement is a vector quantity representing the shortest length between the starting and stopping point. It has both magnitude and directions.

If we differentiate the displacement function with respect to time, we shall get the instantaneous velocity function.

Calculation:

$x = t + 1$

$= > v = \dfrac{dx}{dt}$

$= > v = \dfrac{d(t + 1)}{dt}$

$= > v = \dfrac{d(t)}{dt} + \dfrac{d(1)}{dt}$

$= > v = 1 + 0$

$= > v = 1 \: unit$

So the object is following uniform motion with constant velocity.

Answer 2

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.