First slide

Rectilinear Motion

Question

The displacement of a body from a reference point, is given by $\sqrt{x} = 2 t + 3$ where x is in meter and t in seconds. This shows that the body is

Moderate

A

at rest
B

accelerated
C

decelerated
D

in uniform motion

Solution

Squaring both sides, we have $x = 12 t + 4 t^{2} + 9$
Since displacement x changes with time t, the body cannot be at rest. The velocity of the body is given by $v = \frac{dx}{dt} = 12 + 8 t$
Since the velocity v changes with time t, the body is not in uniform motion; it is accelerated because v increases with t.

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