Question

A displacement-time graph of a body moving with uniform velocity is shown in the figure. Find out its velocity and its displacement at the end of 5 seconds.
 

A.10 m/s, 125m
B.5 m/s, 225m
C.3m/s, 15m
D.15m/s, 75m

Answer 1

Hint: The displacement-time graph shows that the displacement of the moving object changes with respect to the time. The horizontal lines on a displacement time graph shows that the object is stationary.

Complete answer:
We have to find the velocity and the displacement at the end of 5 seconds.
Here, we look at the distance-time graph and observe that the displacement is 15m when there is a time of 5 seconds.
Now, we have to calculate the velocity.
The velocity is the rate of change of the displacement. That means if we divide the displacement from time then we get the value of the velocity.
But there is a coordinate so we calculate the velocity via slope.
The slope helps us to find the ratio of the vertical change to the horizontal change.
So, the vertical direction is the displacement and the horizontal direction there is a time.
We observe the final displacement and the final time and initial displacement and initial time too.
The expression for slope is
$Slope={\displaystyle \frac{\mathrm{\Delta }vertical}{\mathrm{\Delta }horizontal}}$
Here the final displacement = 15m
Initial displacement = 0m
Final time = 5s
Initial time = 0s
$velocity={\displaystyle \frac{\mathrm{\Delta }displacement}{\mathrm{\Delta }time}}$
$v={\displaystyle \frac{15-0}{5-0}}$
$\Rightarrow v={\displaystyle \frac{15}{5}}$
$v=3m/s$
So, the velocity is 3m/s and the displacement is 15m

So, the option (C) is correct.

Note:
The difference between the displacement time graph and the velocity – time graph.
In, Displacement-time graph at any point on a graph has a coordinate of (time, distance), the SI unit of the displacement is meter and the SI unit of time is second.
In, Velocity-time graphs. Any point on such a graph will have coordinates (time, velocity), the SI unit of the velocity is meter per second and the SI unit of time is second.