Question

The kinetic energy of a particle continuously increases with time

• A. The resultant force on the particle must be parallel to the velocity at all instants.
• B. The resultant force on the particle must be at an angle greater than ${90}^o$ with the velocity at all time.
• C. Its height above the ground level must continuously decreases.
• D. The magnitude of its linear momentum is increasing continuously.

Answer 1

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

The correct options are
A The resultant force on the particle must be parallel to the velocity at all instants.
C Its height above the ground level must continuously decreases.
D The magnitude of its linear momentum is increasing continuously.

Justification for "The resultant force on the particle must be parallel to the velocity at all instants"

If resultant force is parallel to the velocity then $|\overrightarrow{V}|$ will increase.

$\therefore K.E=\frac{1}{2}m|\overrightarrow{V}{|}^2$ will increase with time.

Justification for "Its height above the ground level must continuously decreases."

Energy Cnservation:

$P{E}_i-P{E}_f=K{E}_f-K{E}_i$

If height decrease $P{E}_i-P{E}_f=$ Increase.

$\therefore K{E}_f-K{E}_i=$ Increase.

Where $P{E}_i=$ Potential energy initially.

$P{E}_f=$ Potential energy finally.

$K{E}_i=$ Kinetic Energy Initially.

$K{E}_f=$ Kinetic Energy Finally.

Justification for "The magnitude of its linear momentum is incease continiously."

$KE=\frac{1}{2}V\left(mV\right)$

$=\frac{1}{2}V|\overrightarrow{P}|$

$\therefore KE$ increases with time