Question

A body of mass $m$ accelerates uniformly from rest to $v_{1}$ in time $t_{1}$ . The instantaneous power delivered to the body as a function of the $t$ is

• A. $\frac{m v_{1} t ⁡}{t ⁡_{1}}$
• B. $\frac{m v_{1}^{2} t ⁡}{t ⁡_{1}^{2}}$
• C. $\frac{m v_{1} t ⁡^{2}}{t ⁡_{1}}$
• D. $\frac{m v_{1}^{2} t ⁡}{t ⁡_{1}}$

Answer 1

Answer: (B)

Acceleration $a=\frac{v_{1}}{t _{1}}$
$\therefore \text{Velocity}\left(\right.v\left.\right)=0+at =\frac{v_{1}}{\left(t ⁡\right)_{1}}t⁡$
Power $P =\text{Force}\times \text{velocity}=m⁡av$
or $P=m\left(\frac{v_{1}}{t_{1}}\right) \times\left(\frac{v_{1} t}{t_{1}}\right)=\frac{m v_{1}^{2} t}{t_{1}^{2}}$