First slide

Rectilinear Motion

Question

An insect moving along a straight line, travels in every second distance equal to the magnitude of time elapsed. Assuming acceleration to be constant, and the insect starts
at t = 0. Find the magnitude of initial velocity of insect

Moderate

A

$\frac{3}{2} unit$
B

$\frac{5}{4} unit$
C

$2 unit$
D

$\frac{1}{2} unit$

Solution

Distance travelled from time t - 1 sec to t sec is
$\begin{array}{l} S = u + \frac{a}{2} (2 t - 1) . . . . . . . (i) \\ from given condition S = t . . . . . . (i i) \\ (i) and (ii) \Rightarrow t = u + \frac{a}{2} (2 t - 1) \\ \Rightarrow u = \frac{a}{2} + t (1 - a) \end{array}$
Since u and a are arbitrary constants, and they must be constant for every time.
$\Rightarrow Coefficient of t must be equal to zero.$
$\Rightarrow 1 - a = 0 \Rightarrow a = 1 for a = 1, u = \frac{1}{2} unit$
$Initial speed is \frac{1}{2} unit.$

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