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

Answer 1

Answer: (A)

$10 \,cm \,s^{-1}$

Answer 2

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