Instantaneous Power — Prelims Questions

A particle moves with a velocity $\vec{v} = (3\hat{i} + 4\hat{j})\text{ m/s}$ under the influence of a constant force $\vec{F} = (5\hat{i} - 2\hat{j})\text{ N}$. What is the instantaneous power delivered by the force?

A body of mass $2\text{ kg}$ is moving such that its position $x$ as a function of time $t$ is given by $x(t) = 3t^2 - 2t + 5\text{ m}$. What is the instantaneous power delivered to the body at $t = 1\text{ s}$ by the net force acting on it?

A force $\vec{F} = (6t\hat{i} + 8\hat{j})\text{ N}$ acts on a particle. The particle moves with a constant velocity $\vec{v} = (2\hat{i} + 3\hat{j})\text{ m/s}$. What is the instantaneous power delivered by the force at $t = 2\text{ s}$?

Which of the following statements about instantaneous power is INCORRECT?

A block of mass $m$ is pulled along a horizontal surface by a constant force $F$ acting at an angle $\theta$ with the horizontal. If the block moves with a constant velocity $v$, what is the instantaneous power delivered by the applied force?

A particle of mass $m$ is projected vertically upwards with an initial velocity $u$. Neglecting air resistance, what is the instantaneous power delivered by gravity when the particle is at its highest point?