Question

The acceleration of a moving body is found from the:

• A. area under velocity-time graph
• B. area under displacement-time graph
• C. slope of distance-time graph
• D. slope of velocity-time graph
• E. area under acceleration-time graph

Hint:

To remember graphical relations:
Displacement $\rightarrow$ Velocity (Slope)
Velocity $\rightarrow$ Acceleration (Slope)
Acceleration $\rightarrow$ Velocity (Area)
Velocity $\rightarrow$ Displacement (Area).

Answer 1

The Correct Option is D

To determine the acceleration of a moving body, we need to analyze its velocity-time graph. The acceleration is defined as the rate of change of velocity with respect to time. This can be mathematically represented as:

\(\text{Acceleration} = \frac{\Delta \text{Velocity}}{\Delta \text{Time}}\)

Given this definition, the acceleration corresponds to the slope of the velocity-time graph because the slope of any graph is the change in the vertical axis divided by the change in the horizontal axis.

Analysis of Options:

1. Area under velocity-time graph : This represents the displacement of the body, not acceleration.
2. Area under displacement-time graph : This is not a standard calculation in kinematics as displacement-time graphs are typically used to find velocity, not acceleration.
3. Slope of distance-time graph : This gives velocity, not acceleration, as it represents the change in distance over time.
4. Slope of velocity-time graph : This is the correct answer, as it directly provides the acceleration.
5. Area under acceleration-time graph : This represents the change in velocity, not the acceleration itself.

The correct answer is, therefore, the slope of the velocity-time graph. This understanding plays a crucial role in physics, aiding in the analysis of motion and kinematic equations.