Question

A body of mass $5\, kg$ under the action of constant force $\vec{F}=F_{x} \hat{i} +F_{y} \hat{j}$ has velocity at $t = 0\,s$ as $\vec{\upsilon} = \left(6\hat{i} - 2\hat{j}\right)$ m/s and at $t = 10 s$ as $\vec{\upsilon}=+6 \hat{j}$ m/s. The force $\vec{F}$ is :

• A. $\left(-3\hat{i} + 4\hat{j}\right) N$
• B. $\left(-\frac{3}{5}\hat{i} + \frac{4}{5}\hat{j}\right) N$
• C. $\left(3\hat{i} - 4\hat{j}\right) N$
• D. $\left(\frac{3}{5}\hat{i} - \frac{4}{5}\hat{j}\right) N$

Answer 1

Answer: (A)

$\left(-3\hat{i} + 4\hat{j}\right) N$

Answer 2

$F = \frac{m\left(v_{f} - v_{i}\right)}{t}$
$= \frac{5\left(6\hat{j}-6\hat{i}+2\hat{j}\right)}{10} = \frac{40\hat{j}-30\hat{i}}{10} = -3\hat{i}+4\hat{j}$