Question

A $3\, kg$ object has initial velocity $\left(6\hat{i}-2\hat{j}\right)m/s.$ The total work done on the object if its velocity changes to $\left(8\hat{i}-4\hat{j}\right)m/s$ is

• A. $60J$
• B. $120J$
• C. $216J$
• D. $44J$

Answer 1

Answer: (A)

The net workdone on the object is equal to the change in the kinetic energy of the object
$W_{net}=K_{f}-K_{i}=\Delta K$
Kinetic energy $K=\frac{1}{2} m v^{2}$
Velocity $v^{2}=v_{x}^{2}+v_{y}^{2}$
$=(36+4) m / s^{2}$
$v^{2}=40\, m / s ^{2}$
$K_{i}=\frac{1}{2} \times 3 \times 40=60\, J$
Again velocity $v=\sqrt{8^{2}+4^{2}}$
$v=\sqrt{64+16}=\sqrt{80}$
Kinetic energy $K_{f}=\left(\frac{1}{2}\right)(3) \times 80\, m / s ^{2}=120\, J$
From work energy theorem
$W_{\text {net }} =K_{f}-K_{i}$
$=120\, J -60\, J =60\, J$