Question

A body with mass 5 kg is acted upon by a force

$\overrightarrow{F} = \left( - 3\widehat{i} + 4\widehat{j} \right)$N. if its initial velocity at t = 0 is

$\overrightarrow{u} = \left( 6\widehat{i} - 12\widehat{j} \right)ms^{- 1}$ the time at which it will just have a velocity along the y – axis is.

• A. 0
• B. 10 s
• C. 2 s
• D. 15 s

Answer 1

Answer: (B)

10 s

Answer 2

Here $m = 5kg,\overset{\rightarrow}{F} = - 3\overset{\land}{i} + 4\overset{\land}{j}N$

$\overset{\rightarrow}{u} = - 6\overset{\land}{i} - 12\overset{\land}{j}ms^{- 1}$

The acceleration of the body is

$\overset{\rightarrow}{a} = \frac{\overset{\rightarrow}{F}}{m} = \frac{( - 3\overset{\land}{i} + 4\overset{\land}{j})N}{5kg} = - \frac{3}{5}\overset{\land}{i} + \frac{4}{5}\overset{\land}{j}ms^{- 2}$

Velocity of the body along x-axis at any time t is

$v_{x} = u_{x} + a_{x}t = 6 - \frac{3}{5}t$

As the body will have a velocity along y-axis, therefore its velocity along x-axis will be zero

i.e. $v_{x} = 0or6 = \frac{3}{5}t \Rightarrow t = \frac{30}{3} = 10s$