First slide

Instantaneous velocity

Question

The equation $\sqrt{x} =t+3$ gives the variation of displacement x with time t for a particle moving along the X-axis. Which of the following is correct for the motion of the particle?

Easy

A

velocity the particle is directly proportional to time
B

velocity of the particle is inversely proportional to time
C

the particle has time varying acceleration
D

the acceleration of the particle is constant

Solution

Squaring the equation gives $x = t^{2} + 6 t + 9$ . On differentiation, $v = 2 t + 6$ and $a = 2 .$ First option is a good trap, $v = 2 t + 2$ cannot be interpreted as $v α t$ . Only the acceleration is constant

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