Ncert Exercises & Solutions

A body with a mass of \(5\) kg is acted upon by a force \(\vec{F}=( -3\hat{i} +4\hat{j})\) N. If its initial velocity at \(t=0\) is \(\vec{v}= ( 6\hat{i} -12\hat{j} )\) m/s, the time at which it will just have a velocity along the \(y\)-axis is:
1. never
2. \(10\) s
3. \(2\) s
4. \(15\) s

Hint: The final velocity along the \(x\)-axis is equal to zero.

Step: Find the time at which the body will just have a velocity along the \(y\)-axis.
As the velocity only along the \(y\)-axis, then the final velocity along the \(x\)-axis is equal to zero.
Now, we can resolve the components of force and obtain \(a_x.\)
Then, \(a_x=\dfrac{F_x}{m}=\dfrac{-3}{5}~\text{m/s}^2\)
Using, \(v=u+at\)
\(\Rightarrow 0=6+\left(\dfrac{-3}{5}\right)t \)
\(\Rightarrow t=10~\text s\)
Hence, option (2) is the correct answer.

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