Question

An object of mass 3 kg is at rest. Now a force of \(\vec{F} = 6 t^2 \hat{i} + 4t \hat{j}\) is applied on the object then velocity of object at r = 3 second is :-

• A. $ 18 \widehat{i} + 3 \widehat{j}$
• B. $ 18 \widehat{i} + 6 \widehat{j}$
• C. $ 3 \widehat{i} + 18 \widehat{j}$
• D. $ 18 \widehat{i} + 4 \widehat{j}$

Answer 1

The Correct Option is B

The correct answer is B:\(18 \,\hat{ i }+6\, \hat{ j }\)
 \(\vec{ a }=\frac{\vec{ F }}{ m }=2 t ^{2} \hat{ i }+\frac{4}{3} t \hat{ j }\)
\(d \vec{ v }=\left(2 t ^{2} \hat{ i }+\frac{4}{3} t \hat{ j }\right) dt\)
Integrate on both sides 
\(\vec{ v }=2\left[\frac{ t ^{3}}{3}\right] \hat{ i }+\frac{4}{3}\left[\frac{ t ^{2}}{2}\right] \hat{ j }\)
at \(t =3 \,sec\)
\(\vec{ v }=\frac{2}{3}(3)^{3} i +\frac{4}{6}(3)^{2} \hat{ j }\)
\(=18 \,\hat{ i }+6\, \hat{ j }\)