Everything Science Grade 10

21.6 CHAPTER 21. MOTION IN ONE DIMENSION

Since we know that velocity is the rate of change of position, we can confirm the value for

the velocity vs. time graph, by calculating the gradient of the~xvs.tgraph.

Tip

The gradient of a po-
sition vs. time graph
gives the average ve-
locity, while the tan-
gent of a position vs.
time graph gives the
instantaneous veloc-
ity.

If we calculate the gradient of the~xvs.tgraph for a stationary object we get:

v=∆∆~xt

=~xtf−~xi

f−ti

= 1202 ms−−^260 ms(initial position=final position)

= 0m·s−^1 (for the time that Vivian is stationary)

Similarly, we can confirm the value of the acceleration by calculating the gradient of the

velocity vs. time graph.

Tip

The gradient of a ve-
locity vs. time graph
gives the average ac-
celeration, while the
tangent of a velocity
vs. time graph gives
the instantaneous ac-
celeration.

If we calculate the gradient of the~vvs.tgraph for a stationary object we get:

a=∆∆vt

=~vtf−~vi

f−ti

=^0 m·s

− (^1) − 0 m·s− 1
120 s− 60 s
= 0m·s−^2
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.
Tip
The area under the
velocity vs. time
graph gives the
displacement.
The displacement of the object is given by the area under the graph, which is 0 m. This is
obvious, because the object is not moving.
Motion at Constant Velocity ESAHC
Motion at a constant velocity oruniform motionmeans that the position of the object is
changing at the same rate.
Assume that Vivian takes 100 s to walk the 100 m to the taxi-stop every morning. If we
assume that Vivian’s house is the origin and the direction to the taxi is positive, then
408 Physics: Mechanics