Question

A body of mass $5kg$ under the action of constant force $\overrightarrow{F}=F_x\hat{i}+F_y\hat{j}$ has velocity at $t=0s$ as $\overrightarrow{v}=(6\hat{i}-2\hat{j})m/s$ and at $t=10s$ as $\overrightarrow{v}=+6\hat{j}m/s$. The force $\overrightarrow{F}$ is:

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

Answer 1

Answer: (A)

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

Given,

${\overrightarrow{v}}_i=(6\hat{i}-2\hat{j})m/s$ at $t=0sec$

${\overrightarrow{v}}_f=6\hat{j}m/s$ at $t=10sec$

$m=5kg$

Constant force, $F=\frac{dP}{dt}$

$F=m\frac{dv}{dt}$

$F=5\frac{{\overrightarrow{v}}_f-{\overrightarrow{v}}_i}{t_f-t_i}$

$F=5\frac{\left(6\hat{j}\right)-(6\hat{i}-2\hat{j})}{10}$

$F=\frac{-6\hat{i}+8\hat{j}}{2}$

$F=(-3\hat{i}+4\hat{j})$

The correct option is A.