0.2 Motion in one dimension  (Page 9/16)

If we calculate the gradient of the $v$ vs. $t$ graph for a stationary object we get:

Additionally, because the velocity vs. time graph is related to the position vs. time graph, we can use the area under the velocity vs. time graph to calculate the displacement of an object.

The displacement of the object is given by the area under the graph, which is $0\mathrm{m}$ . This is obvious, because the object is not moving.

Motion at constant velocity

Motion at a constant velocity or uniform motion means that the position of the object is changing at the same rate.

Assume that Lesedi takes $100\mathrm{s}$ to walk the $100\mathrm{m}$ to the taxi-stop every morning. If we assume that Lesedi's house is the origin, then Lesedi's velocity is:

Lesedi's velocity is 1 m $·$ s ${}^{-1}$ . This means that he walked $1\mathrm{m}$ in the first second, another metre in the second second, and another in the third second, and so on. For example, after $50\mathrm{s}$ he will be $50\mathrm{m}$ from home. His position increases by $1\mathrm{m}$ every $1\mathrm{s}$ . A diagram of Lesedi's position is shown in [link] .

We can now draw graphs of position vs.time ( $x$ vs. $t$ ), velocity vs.time ( $v$ vs. $t$ ) and acceleration vs.time ( $a$ vs. $t$ ) for Lesedi moving at a constant velocity. The graphs are shown in [link] .

In the evening Lesedi walks $100\mathrm{m}$ from the bus stop to his house in $100\mathrm{s}$ . Assume that Lesedi's house is the origin. The following graphs can be drawn to describe the motion.

We see that the $v$ vs. $t$ graph is a horisontal line. If the velocity vs. time graph is a horisontal line, it means that the velocity is constant (not changing). Motion at a constant velocity is known as uniform motion .

We can use the $x$ vs. $t$ to calculate the velocity by finding the gradient of the line.

Lesedi has a velocity of $-1\mathrm{m}·\mathrm{s}{}^{-1}$ , or $1\mathrm{m}·\mathrm{s}{}^{-1}$ towards his house. You will notice that the $v$  vs.  $t$ graph is a horisontal line corresponding to a velocity of $-1\mathrm{m}·\mathrm{s}{}^{-1}$ . The horizontal line means that the velocity stays the same (remains constant) during the motion. This is uniform velocity.

We can use the $v$ vs. $t$ to calculate the acceleration by finding the gradient of the line.

Lesedi has an acceleration of $0\mathrm{m}·\mathrm{s}{}^{-2}$ . You will notice that the graph of $a$ vs. $t$ is a horisontal line corresponding to an acceleration value of $0\mathrm{m}·\mathrm{s}{}^{-2}$ . There is no acceleration during the motion because his velocity does not change.

We can use the $v$ vs. $t$ to calculate the displacement by finding the area under the graph.