Question

A body of mass $3kg$ moving with a constant acceleration covers a distance of $10m$ in the $3^{rd}$ second and $Ibm$ in the $4^{th}$ second respectively. The initial velocity of the body is:

• A. $10m{s}^{-1}$
• B. $8m{s}^{-1}$
• C. $5m{s}^{-1}$
• D. $-5m{s}^{-1}$

Answer 1

The correct option is D $-5m{s}^{-1}$

Given that,

Mass of body = $3kg$

Distance covered in nth second = $u+a/2 (2n-1)$
initial velocity = $u$
nth second = $n$
acceleration = $a$

Now, distance covered in 3rd second =$10\ m$

$10=u+\frac{a}{2}(2\times 3-1)$

$20=2u+5a....\left(I\right)$

Now, distance covered in 4rd second= 16 m

$16=u+\frac{a}{2}(2\times 4-1)$

$32=2u+7a...\left(II\right)$

Now, from equations (I) and (II)

$-12=-2a$

$a=6m/s^2$

Now, put the value of a in equation (I)

$20=2u+5a$

$2u=20-30$

$u=-5m/s$

Hence, the initial velocity is $-5m/s$