A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to:

Question

A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to: (A)  t1/2  (B)  t3/4  (C)  t  (D)  t3/2

Tardigrade Admin · Accepted Answer

Power (P)=[ML2T-3] ∴ [L2]=(P/[MT-3])=[PM-1T3] As P and M are constant, therefore L2 propto T3 ⇒ L propto T3/2 ⇒ The distance moved by the body in time t is proportional to t3/2 .

Q. A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to:

$t^{1/2}$

$t^{3/4}$

$t$

$t^{3/2}$

$t^{2}$

Power $(P) = [M L^{2} T^{- 3}]$ $∴$ $[L^{2}] = \frac{P}{[ M T ^{- 3} ]} = [P M^{- 1} T^{3}]$ As P and M are constant, therefore $L^{2} \propto T^{3}$ $\Rightarrow$ $L \propto T^{3/2}$ $\Rightarrow$ The distance moved by the body in time t is proportional to $t^{3/2}$ .

Q. A body at rest is moved along a straight line by a machine which delivers constant power. The distance moved by the body in time t is proportional to:

t1/2

t3/4

t

t3/2

t2

Power (P)=[ML2T−3] ∴ [L2]=[MT−3]P​=[PM−1T3] As P and M are constant, therefore L2∝T3 ⇒ L∝T3/2 ⇒ The distance moved by the body in time t is proportional to t3/2 .

$t^{1/2}$

$t^{3/4}$

$t$

$t^{3/2}$

$t^{2}$

Power $(P) = [M L^{2} T^{- 3}]$ $∴$ $[L^{2}] = \frac{P}{[ M T ^{- 3} ]} = [P M^{- 1} T^{3}]$ As P and M are constant, therefore $L^{2} \propto T^{3}$ $\Rightarrow$ $L \propto T^{3/2}$ $\Rightarrow$ The distance moved by the body in time t is proportional to $t^{3/2}$ .