Question

A body covers $200cm$ in the first $2$ sec.and $220cm$ in next $4$ sec. What is the velocity of the body at the end of $7th$ second

• A. $40cm/sec$
• B. $20cm/sec$
• C. $10cm/sec$
• D. $5cm/sec$

Answer 1

The correct option is C $10cm/sec$

$\text{Step 1: Applying equation of motion}$

Since acceleration is constant, therefore we can apply equation of motion.

$\text{In first case:}$ When body covers $200cm$ in $2s$:

$s_1=u{t}_1+\frac{1}{2}a{t}_1^2$

$\Rightarrow$ $200=u\left(2\right)+\frac{1}{2}a(2{)}^2$

$\Rightarrow$ $a+u=100$ $....\left(1\right)$

$\text{In second case:}$ Total displacement, $s_2=200cm+220cm=420cm$

Total time: $t_2=2s+4s=6s$

$s_2=u{t}_2+\frac{1}{2}a{t}_2^2$

$\Rightarrow 420=u\left(6\right)+\frac{1}{2}a(6{)}^2$

$\Rightarrow$ $u+3a=70$ $....\left(2\right)$

$\text{Step 2: Initial velocity and acceleration}$

Subtracting $e{q}^n\left(1\right)$ from $\left(2\right)$

$2a=-30\Rightarrow a=-15cm/s^2$

Putting the value of $a$ in equation $\left(1\right)$ we get, $u=115cm/s$

$\text{Step 3: Velocity at the end of 7th second}$

Velcity at the end of $7th$ second:

$v=u+at$ $=115-15\times 7$$=10cm/s$

Hence, Option $C$ is correct.