Question

The slope of displacement-time graph gives
(A) Distance
(B) Velocity
(C) Acceleration
(D) None of these

Answer 1

Here using the formula of slope, we can state the correct option. Slope of a graph is represented as the ratio of change in y axis to change in x axis at that particular point of changed y value. Here our y axis is the displacement and the x- axis is the time. Now with the slope concept we can find the answer.

Complete answer:
First see the diagram given below to get a better view to the problem,

Here the displacement time graph, the y-axis represents the displacement while the x-axis represents the time.
We know that slope of a graph is defined as the ratio of change in y aix to ratio of change in x-axis at that particular value of y.
Here the change in y axis means change in the displacement along the y axis and change in x-axis means change in time at the changed values of displacement.
Now mathematically we can write,
$Slope = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{\Delta d}}{{\Delta t}}$
Where,
Change in displacement is equal to $\Delta d$.
Change in time is equal to $\Delta t$.
Hence the solve of displace time graph gives the velocity which is the ratio of change displacement to change time.
Therefore, the correct option is $\left( B \right)$.

Note:
If the slope is positive then it indicates that the body is moving away from the reference line or we can say from the starting point and if the slope is negative then the body is reverting to the initial point which is just opposite to positive slope. Never confuse between distance time graph and displace time graph because distance time graph gives speed as distance itself is a scale quantity.