Question

The displacement of a body along x axis depends on time as x^1/2=t+1. Then the velocity of body is

Answer 1

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ANSWER::

√x = t + 1

Squaring both sides

(√x)² = (t + 1)²

x = t² + 2t + 1

Now , lets apply differentiation

dx/dt = (d/dt)(t² + 2t + 1) = 2t + 2

Now , we will put some values in t to check which option is right.

We won't take t values negative because time cannot be negative.

v(t) = 2t + 2

v(0) = 2(0) + 2 = 2

v(1) = 2(1) + 2 = 4

v(2) = 2(2) + 2 = 6

After putting values we can see that the velocity is increasing as time increases .

(a) Increases with time will be the answer.