A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as [This question includes concepts from Work, Energy and Power chapter]

1. $P<mspace\; width="1em"></mspace>\propto <mspace\; width="1em"></mspace>t^2$

2. $P<mspace\; width="1em"></mspace>\propto <mspace\; width="1em"></mspace>t$

3. $P<mspace\; width="1em"></mspace>\propto \sqrt{<mspace\; width="1em"></mspace>t}$

4. $P<mspace\; width="1em"></mspace>\propto <mspace\; width="1em"></mspace>t^{3/2}$

A body starts moving from rest in straight line under a constant power source. Its displacement in time t is proportional to

1. $t^{1/2}$

2. t

3. $t^{3/2}$

4. $t^2$

The relation between velocity (v) and time (t) is $v\propto \sqrt{\mathrm{t}}$, then which one of the following quantity is constant?

1.  Force

2.  Power

3.  Momentum

4.  Kinetic Energy

A particle is moving on the circular path of the radius (R) with centripetal acceleration $a_c=k^{2}R{t}^2$. Then the correct relation showing power (P) delivered by net force versus time (t) is 

1. 1

2. 2

3. 3

4. 4

A body is displaced from (0,0) to (1m,1m) along the path x=y by a force $F=\left(x^2\hat{j}+y\hat{i}\right)N$. The work done by this force will be :

1. $\frac{4}{3}J$

2. $\frac{5}{6}J$

3. $\frac{3}{2}J$

4. $\frac{7}{5}J$

A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be

1.  ${\mathrm{Fv}}^2$

2.  Fv

3.  $\mathrm{F}/{\mathrm{v}}^2$

4.  F/v

A particle moves from position ${\overrightarrow{r}}_1=3\hat{i}+2\hat{j}-6\hat{k}$ to position ${\overrightarrow{r}}_2=14\hat{i}+13\hat{j}+9\hat{k}$ under the action of force $4\hat{i}+\hat{j}+3\hat{k}N.$ The work done will be 

(1) 100 J

(2) 50 J

(3) 200 J

(4) 75 J

An ice cream has a marked value of 700 kcal. How many kilowatt- hour of energy will it deliver to the body as it is digested 

(1) 0.81 kWh

(2) 0.90 kWh

(3) 1.11 kWh

(4) 0.71 kWh

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

(1) $\frac{m{v}_{1}t}{t_1}$

(2) $\frac{m{v}_1^{2}t}{t_1}$

(3) $\frac{m{v}_1{t}^2}{t_1}$

(4) $\frac{m{v}_1^{2}t}{t_1^2}$

A weight lifter lifts 300 kg from the ground to a height of 2 meter in 3 second. The average power generated by him is 

(1) 5880 watt

(2) 4410 watt

(3) 2205 watt

(4) 1960 watt