Question

A girl walks along a straight path to drop a letter in the letterbox and comes back to her initial position. Her displacement-time graph is shown in figure. Plot a velocity-time graph for the same.

Answer 1

Hint:We will use the formula which gives velocity i.e. velocity is defined as displacement per unit time. As the displacement increases, the velocity is positive. Velocity is taken to be negative as the displacement decreases. Positive velocity will be plotted above the horizontal axis. Negative velocity is plotted below the horizontal axis.

Formula used:
Using velocity formula,
\[v = \dfrac{{\Delta d}}{{\Delta t}}\] …… (1)
Where,
\[v\] is velocity
\[\Delta d\] is displacement
\[\Delta t\] is changing in time.

Complete step by step answer:
From the graph we know that, velocity time graph is a straight line and the velocity of the girl is constant.Here, displacement is \[\Delta d = 100\], and \[\Delta t = 50\].So,For the initial \[50\,{\text{s}}\] , the velocity will be,
$v = \dfrac{{\Delta d}}{{\Delta t}} \\
\Rightarrow v = \dfrac{{100}}{{50}} \\
\Rightarrow v = 2\,{\text{m}}/{\text{s}} \\$
And the next \[50\,{\text{s}}\] the velocity is taken in negative because displacement is becoming zero,
$v = \dfrac{{\Delta d}}{{\Delta t}} \\
\Rightarrow v = \dfrac{{0 - 100}}{{50}} \\
\therefore v = - 2\,{\text{m}}/{\text{s}}$
Therefore, the velocity-time graph is as shown in the figure below.

Additional information:
Velocity: The velocity of an object, with respect to a frame of reference, is the rate of change of its position and is a function of time. Velocity is equal to the speed and direction of motion of an object specification. In kinematics, the branch of classical mechanics that explains the motion of bodies, velocity is a basic concept.

Note:Remember that a negative acceleration implies that in the negative direction, the change in the velocity points. The velocity may be in the positive direction, for example, and the object will slow down or the velocity could be in the negative direction and the object will speed up. Velocity tracks motion beginning in one position and continuing to another. There are countless functional velocity uses, but one of the most common reasons for calculating velocity is to determine how quickly you (or something in motion) will arrive from a given position at a destination. The factors influencing an object's terminal velocity include its mass. Gravity-due acceleration, \[g\] .