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a speedometer
Average speed
Average speed
A moving object's average speed is the total distance travelled divided by the total time elapsed. The speedometer of a vehicle tells its speed in kilometres/hour (km/s). But the SI unit for speed is in metre/second (m/s).
Knowing the distance travelled and the time an object took to travel the distance allows to calculate the object's average speed with the equation: vav = Δd/Δt
vav = average speed
Δd = distance travelled
Δt = change in time
Both distance and speed are scalar quantities, a physical quantity that's utterly described by its magnitude (some others are density, energy, mass, and time).
The following section shows how to use the equation to find the object's average speed.
Example 1
Example 1
A dog runs in a straight line of 43m in 28s. What's his average speed?
43m = Δd
28s = Δt
vav = 43 / 28
vav = 1.54 m/s is the dog's average speed?
Average velocity
Average velocity
An object in motion's average velocity is its total displacement/position change, divided by the total time taken for the motion.
displacement: measure of speed and direction
Not to be confused with average speed.
Average speed shows an object's speed no matter its direction, while average velocity shows both speed and direction, a more complete motion description.
In short, direction doesn't matter in speed but does in displacement.
Velocity describes position change overtime.
For instance, a bike travelling east at a constant speed of 11 m/s has a velocity of 11 m/s [E]. Since it has direction and magnitude, average velocity is a vector quantity.
→
The SI unit for velocity is metre per second (m/s). Its symbol is vav.
This method can be used whether the graph passes through the origin or not.
Position-time graph
Position-time graph
A position-time graph describes an object's motion, with a position on the y-axis and time on the x-axis.
Figure 2 shows a position-time graph for students' motion of a rolling measure in an experiment. See that the points on the graph form a straight line moving upward from left to right. When an object moves at constant velocity, its graph is a straight line.
Like in math, its slope (m) describes its steepness, calculated as shown in Figure 2, by comparing the magnitude of rise (change between points of y-axis) and the run's magnitude (change between points of x-axis).
E.g. In Figure 3, the motion starts at 10m [E] when t = 0 s. For an object moving at a constant velocity, so that's the position-time graph is a straight line, the key relationship is this: the position-time graph's slope shows an object's velocity.
Steeper the graph, greater the object's displacement in a given time interval and higher its velocity, which can be confirmed using the info in Figure 2.
Like in math, Δd, the graph's slope formula is either
→ →
Δd2 - d1 →
slope = rise/run, or m = ________ , or m = Δd / Δt
t2 - t1
The equation gives a moving object's average velocity:
→
→ Δd
vav = ___
Δt
To determine the slope (average velocity) from the zero point to the final data point for the x-axis and y-axis for the motion in Figure 2, substitute the initial and final displacement and time values into the derived equation:
The rolling ball's velocity is 4 m/s [E]. Note that the graphs' slope in Figure 2 and 3 are the same, 4 m/s [E]. The 2 motions are different in that the motion in Figure 2 started 0 m away from the observer, whereas the motion in Figure 3 has an initial position of 10 m [E] from the observer. Calculating average velocity from the slope of a position-time graph is a very useful method as it's often hard to measure directly. But position can be easily done with equipment like tape measures, motion sensors, and laser speed devices.
Velocity (a vector quantity) is to speed (a scalar quantity) as displacement (a vector quantity) is to distance (a scalar quantity). The average velocity equation should thus be similar to the one for average speed, but velocity and displacement are vectors:
Average velocity Example 1
Average velocity Example 1
Calculate the average velocity of the balloon: A balloon's position changes as the windy blows it 82 m [N] away from a child in 15s.
Solution:
Substitute the displacement (82 m) and time (15 s.) into the average velocity equation:
→
→ Δd
vav = ___
Δt
→
→ 82
vav = ___
15
vav = 5.5 m/s [N] is the average the ballon's velocity.
Average velocity Example 2
Average velocity Example 2
A train travels at an average velocity of 22.3 km/h [W].
How long (Δt) will the train go in a displacement of 241 m [W]?
Solution:
Substitute the average velocity (22.3 km/h) and the displacement (241m.) into the average velocity equation to calculate the time (Δt) it will take for the train to go 241 m:
241
22.3 = ____
Δt
Since the measurement units aren't the same, displacement is converted from kilometers/hours to meters/seconds by either being...
multiplied by ratios of 1
22.3 km x 1000 = 22300 meters 22300 m.
Method 1: _____________________________ = __________
h x 60 x 60 3600 s
or...
by directly multiplying the scale of the required units (1 km = 100 m and 1 h = 3600 s).
Method 2: 22.3 km 1 h. 1 m. 1000 m 22300 m.
________ x ______ x _______ x _________ = _________
h 60 m. 60 s. 1 km 3600 s
241 m
22300 m/h = _______ = 0.01081 meter per hours/38.91600 meter per seconds
Δt
Uniform and non-uniform velocity motion
Uniform and non-uniform velocity motion
Motion with uniform/constant velocity is motion in a straight line.
It's an object's basic motion type, except for being at rest.
Note that both requirements (constant speed and straight line) must be met for its velocity to be uniform.
In contrast, motion with non-uniform velocity is when an object's speed or direction isn't constant, indicating; either speeding up, slowing down, changing direction, or combined.
Examples of motion with uniform and non-uniform velocity are:
Describing type of motions from position-time graph
Describing type of motions from position-time graph
Recall that the slope of a position-time graph gives the velocity of an object. A position-time graph describing constant velocity must be a line as a motion with constant velocity. Thus the slope of the position-time graph must also be constant.
The table below shows 5 position-time graph showing commonly motion types.
Terms typically used
"at rest" = something stop moving (a horizontal line)
"negative" position = the line is below the x-axis
"positive" position = the line is above the x-axis
"stationary" = the line is horizontal/speed is constan
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