Question

Starting from rest, a particle is imparted a constant acceleration of 5 units. For this situation, mark out the correct statement(s).

• A. Velocity-time graph is a straight line passing through origin and having slope of 5 units.
• B. Position-time graph is not a straight line.
• C. Position-time graph is a straight line.
• D. Slope of position-time graph increases as the time increases.

Answer 1

Answer: (A), (B), (D)

Slope of position-time graph increases as the time increases.

The explanation for the correct options:

Option A:

• For constant acceleration difference between velocity is the same throughout the motion. Hence, the velocity-time graph will be a straight line.
• As a particle is imparted a constant acceleration of 5 units and acceleration is equal to the slope of the velocity-time graph. Hence, the slope of the velocity-time graph will be 5 units.

Option B:

• The position of a particle will be different at any instantaneous time as it is in motion and accelerating
• If the position-time graph is a straight line then the velocity will be constant which means the particle is moving but with no acceleration which is not the case in the given problem.

Option D:

• If the slope of the position-time graph increases, the velocity of the particle is increasing.
• As the particle is accelerating, the velocity of the particle will increase with time because $\mathit{v}\mathbf{=}\mathit{u}\mathbf{+}\mathit{a}\mathit{t}$.
• Thus, for an accelerating particle, the slope of the position-time graph increases.

The explanation for the incorrect option:

Option C:

• If the position-time graph is a straight line then the velocity will be constant which means the particle is moving but with no acceleration.

Hence, options A, B, and D are correct.