Question

Power of a force acting on a block varies with time $t$ as shown in figure. Then angle between the force acting on the block and its velocity is $\theta$. Then:

• A. $\theta$ is acute at $t=1s$
• B. $\theta$ is 90 at $t=3s$
• C. $\theta$ is obtuse at $t=7s$
• D. change in kinetic energy from $t=0$, to $t=10s$ is $20J$.

Answer 1

Answer: (A), (C), (D)

The correct options are
A $\theta$ is acute at $t=1s$
C $\theta$ is obtuse at $t=7s$
D change in kinetic energy from $t=0$, to $t=10s$ is $20J$.

Power is the dot product of Force and Velocity.
A) It will be positive when the angle between these vectors is acute
B) It will be negative when it is obtuse.
C) It will be zero, when they are perpendicular to each other.
Here,
From $t=1s$ to $6s$, $P$ has positive value, so the angle is acute.
From $t=6s$ to $10s$, $P$ is negative, angle is obtuse.
The area under the graph denotes the change in energy (KE) of the block or the work done by the force on the block.
So, $KE=Abovearea-belowarea$
$KE=40-20=20J$
Options A,C, and D.