Question

A body covers $200cm$ in the first $2$ seconds and $220cm$ in the next $4$ seconds. The velocity of the body at the end of the $7^{th}$ second is

• A. $10cm/s$
• B. $20cm/s$
• C. $5cm/s$
• D. $30cm/s$

Answer 1

The correct option is A $10cm/s$

Let $u$ and $a$ be the initial velocity and uniform acceleration of the body.

Using $S=ut+\frac{1}{2}a{t}^2$
$\therefore 200=u\left(2\right)+\frac{1}{2}a(2{)}^2$
$100=u+a$ ...(i)
Also $420=6u+\frac{1}{2}a(6{)}^2$
$70=u+3a$ ...(ii)

Solving equations (i) and (ii), we get
$u=115cm/s,a=-15cm/s^2$

Using $v=u+at$
$\therefore v=115+(-15)7=10cm/s$