Question

Slope of a velocity time graph gives:

• A. Distance travelled
• B. Velocity
• C. Acceleration
• D. Displacement

Answer 1

The correct option is C

Acceleration

Correct Answer: Option C

1. The velocity time graph shows the change in velocity with time. The velocity is mapped on the y-axis and time on the x-axis.
2. The slope of a graph is determined by the ratio of difference of coordinates of y-axis and difference of coordinates of x-axis. So, the slope of the velocity-time graph is given as $Slope=\frac{∆V}{∆T}$, where $∆V$ is change in velocity and $∆T$ is change in time.
3. Acceleration is defined as the ratio of change in velocity and change in time. Mathematically, it is expressed as $Acceleration=\frac{∆V}{∆T}$.
4. Thus, $Slope=\frac{∆V}{∆T}=Acceleration$.

Incorrect Answers:

Option A

Distance travelled is the product of velocity and time, $Dis\tan ce=Velocity\times Time$, this is not equal to the slope of velocity-time graph. So, this option is incorrect.

Option B

Velocity is the ratio of distance travelled and time, $Velocity=\frac{Dis\tan ce}{Time}$, this is not equal to the slope of velocity-time graph. So, this option is incorrect.

Option D

Displacement is the product of velocity and time, $Displacement=Velocity\times Time$, this is not equal to the slope of velocity-time graph. So, this option is incorrect.

Hence, option C is correct.