Question

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

• A. $10cm{s}^{-1}$
• B. $20cm{s}^{-1}$
• C. $5cm{s}^{-1}$
• D. $30cm{s}^{-1}$

Answer 1

Answer: (A)

Let u and a be the initial velocity and uniform acceleration of the body.
Using $S=ut+\frac{1}{2}a{t}^2$
$\therefore 200=u\left(2\right)+\frac{1}{2}a{\left(2\right)}^2$
$100=u+a...\left(i\right)$
Also $420=6u+\frac{1}{2}a{\left(6\right)}^2$
$70=u+3a...\left(ii\right)$
Solving equations $\left(i\right)$ and $\left(ii\right)$, we get
$u=115cm{s}^{-1},a=-15cm{s}^{-2}$
Using $\upsilon =u+at$
$\therefore \upsilon =115+\left(-15\right)7=10cm{s}^{-1}$