Question

A body is moving with uniform acceleration. covers $200m$ in the first $2s$ and $220m$ in the next $4s$. Find the velocity in $m/s$ after $7s$.

• A. 10
• B. 15
• C. 20
• D. 30

Answer 1

Answer: (A)

Let the initial velocity $=u$ and acceleration $=a$
In first case $s_1=u{t}_1+\frac{1}{2}a{t}_1^2$
$200=2u+2a\left(\therefore t_1=2s\right)$
$u+a=100$ ... (i)
In second case $s_2=u{t}_2+\frac{1}{2}a{t}_2^2$
$420=6u+18a\left(\therefore t_2=2+4=6s\right)$
$3a+u=70$ ... (ii)
Solving Eqs. (i) and (ii), we get
$a=-15m{s}^{-2}$
and $u=115m{s}^{-2}$
$v=u+at$
$=115-15\times 7=10m{s}^{-1}$