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

Step 1: Understanding the Concept:
Acceleration is defined as the rate of change of velocity with respect to time.
In graphical analysis, the rate of change of one variable with respect to another is represented by the slope of the tangent to the curve at that point.
Step 2: Key Formula or Approach:
The mathematical definition of instantaneous acceleration is: \[ a = \frac{dv}{dt} \] This derivative corresponds to the gradient or slope of a velocity ($v$) versus time ($t$) graph.
Step 3: Detailed Explanation:
In a velocity-time graph, the y-axis represents velocity and the x-axis represents time.
The slope ($\frac{dy}{dx}$) of this graph is $\frac{dv}{dt}$.
According to kinematics, this quantity is equal to the acceleration of the body.
For example, if the graph is a straight line, the acceleration is constant, and its value is given by the slope of that line.
Step 4: Final Answer:
The acceleration of a moving body is obtained from the slope of the velocity-time graph.