First slide

Rectilinear Motion

Question

Moving with uniform acceleration, a body covers 150m during 10s so that it covers 24m during 10th sec. Find the initial velocity

Easy

A

5m/s
B

2m/s
C

3m/s
D

4m/s

Solution

Let initial velocity of the body be u and ‘a’ be its acceleration
Given that S=150m
t=10S
$∴$ From equation $S = u t + \frac{1}{2} a t^{2}$
$150 = u (10) + \frac{1}{2} a {(10)}^{2}$
$\Rightarrow u + 5 a = 15.......... (1)$
And also Distance travelled in 10th sec is 24m i.e $n = 10 & S_{n} = 24 m$
From equation
$\begin{array}{l} ∴ S_{n} = u + a (n - \frac{1}{2}) \\ \Rightarrow 24 = u + a (10 - \frac{1}{2}) \\ \Rightarrow 24 = u + \frac{19}{2} a \\ \Rightarrow 2 u + 19 a = 48 \dots \dots \dots \dots \dots . (2) \end{array}$
On solving (1) & (2)
acceleration $a = 2 m / s^{2} ...... (3)$
And initial velocity $u = 5 m / s$

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