Question

In a velocity time graph, what does the negative slope indicate?
$\text{A}\text{. retardation}$
$\text{B}\text{. acceleration}$
$\text{C}\text{. distance}$
$\text{D}\text{. displacement}$

Answer 1

Hint: Slope of a line at any point is the tangent at that point. Slope of the line in the graph tells us that the direction of the line is increasing or decreasing. In a graph, slope can also be calculated as the ratio of the change in y variable to the change in x variable.

Formula used: Slope =$\dfrac{dy}{dx}$

Complete step by step answer:
Velocity is a vector quantity which tells us that displacement per unit time. Rate of change of velocity is known as acceleration. If acceleration is negative it is also known as retardation or deceleration.
The slope of any line is tangent to that line and is given by
Slope=$\dfrac{dy}{dx}$
Where $dy$denotes change in $y$ variable and $dx$ denotes change in x variable.

For velocity-time graph slope is $\dfrac{dv}{dt}$ which gives the rate of change of velocity with respect to time. Therefore, the slope of the velocity-time graph represents the acceleration of the object.
Hence, if the slope is negative, this means the velocity of the object is decreasing with time.
Now we can conclude that the negative slope of the velocity-time graph indicates retardation.

So, the correct answer is “Option A”.

Additional Information: If slope of velocity-time graph is zero, this means velocity of the object is constant. If an object accelerates with non-uniform acceleration, the slope of the object will be different at different points.
Velocity is represented by the slope of the displacement-time graph.

Note: velocity and acceleration both are vector quantities. A vector quantity has both direction and magnitude. Another type of quantity is scalar quantity. Speed is a scalar. Scalars have only magnitude and no direction.