A body of mass m accelerates uniformly from rest to v1 in time t1 . The instantaneous power delivered to the body as a function of the t is

Question

A body of mass m accelerates uniformly from rest to v1 in time t1 . The instantaneous power delivered to the body as a function of the t is (A) (m v1 t â¡/t â¡1) (B) (m v12 t â¡/t â¡12) (C) (m v1 t â¡2/t â¡1) (D) (m v12 t â¡/t â¡1)

Tardigrade Admin · Accepted Answer

Acceleration a=(v1/t 1) ∴ textVelocity(.v.)=0+at =(v1/(t â¡)1)tâ¡ Power P = textForce× textvelocity=mâ¡av or P=m((v1/t1)) ×((v1 t/t1))=(m v12 t/t12)

Q. 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

$\frac{m v _{1} t}{t _{1}}$

$\frac{m v _{1}^{2} t}{t _{1}^{2}}$

$\frac{m v _{1} t ^{2}}{t _{1}}$

$\frac{m v _{1}^{2} t}{t _{1}}$

Acceleration $a = \frac{v _{1}}{t _{1}}$
$∴ Velocity (v) = 0 + a t = \frac{v _{1}}{( t ) _{1}} t$
Power $P = Force \times velocity = m a v$
or $P = m (\frac{v _{1}}{t _{1}}) \times (\frac{v _{1} t}{t _{1}}) = \frac{m v _{1}^{2} t}{t _{1}^{2}}$

Q. A body of mass m accelerates uniformly from rest to v1​ in time t1​ . The instantaneous power delivered to the body as a function of the t is

t⁡1​mv1​t⁡​

t⁡12​mv12​t⁡​

t⁡1​mv1​t⁡2​

t⁡1​mv12​t⁡​