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 time 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 time t is (A) (m v1 t/t1) (B) (m v12 t/t12) (C) (m v1 t2/t1) (D) (m v12 t/t1)

Tardigrade Admin · Accepted Answer

Acceleration a=(v1/t1) ∴ velocity (v)=0+a t=(v1/t1) t ∴ Power P= Force × velocity =m a v 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 time $t$ 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 $= ma v$
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 time t is

t1​mv1​t​

t12​mv12​t​

t1​mv1​t2​

t1​mv12​t​