Question

Draw a velocity-time graph for a uniformly accelerated motion. What does its slope depict?

Answer 1

Velocity-time graph, Uniform accelerated motion and Slope.

1. Velocity-time graph- This graph shows the relationship between changes in velocity with respect to changes in time.
2. Uniform accelerated motion- The term "uniform acceleration" refers to an item traveling in a straight path with an increase in velocity at equal intervals of time.
3. Slope- The slope of a line is the ratio of the increase in y as x increases by a certain amount.

Graph

1. In the velocity-time graph, we have velocity on the y-axis and time on the x-axis.
2. For a uniform acceleration, the velocity changes uniformly with respect to time.
3. So, the graph will have a uniform straight line.

Slope

The slope of a graph depicts the rate of change in the value of y with respect to the change in the value of x.

$Slope=\frac{dy}{dx}$

Here we have velocity on the y-axis and time on the x-axis.

$Slope=\frac{ChangeinVelocity}{ChnageinTime}$

The rate of change in velocity is known as acceleration, So it can be shown as,

$Acceleration=\frac{ChangeinVelocity}{ChnageinTime}$

So, $Acceleration=Slope$

Hence the slope of the velocity-time graph depicts the acceleration.