Question

The gradient or slope of the distance time graph at any point gives
A. Acceleration
B. Distance
C. Velocity
D. Time

Answer 1

In this question, we need to comment on the result of the gradient or the slope of the distance time graph at any point. For this, we will use the definition of the slope (or gradient) of the curve and try to establish the relation with the given options.

Complete step by step answer:
Slope in distance time graph is given by
$\dfrac{{dx}}{{dt}} = \dfrac{{displacement}}{{time}}$
This is also known as velocity.
Thus the slope of a distance time graph at any point gives the velocity of a particle. It is also known as the displacement per unit time.
Its unit is $m{s^{ - 1}}$ or metre per second.

So, the correct answer is “Option C”.

Additional Information:
Below is the table which shows the quantities represented by the areas and slopes of the different kinematics graphs that is the displacement time graph, velocity time graph and acceleration time graph.

Graphs	Slope	Area
Displacement Time graph	Velocity	--
Velocity Time graph	Acceleration	Displacement
Acceleration Time graph	--	Change in velocity

The slope of acceleration time graph and area of distance time graph doesn’t give any quantity.

Note:
The slope or gradient of a graph is given by $\dfrac{{dy}}{{dx}}$ . This means that the quantity in y-axis is divided by the quantity in x-axis to get the slope. Students generally get confused over the areas and slopes of the different graphs in the kinematics chapter. An easy way is to multiply the quantities in x and y axis when asked the area and to divide the quantity in y axis by the quantity in x axis when asked the slope and get an idea of the quantity accordingly.