2) The velocity of the wheel is increasing
3) The slope is the rate of change of velocity
4) The unit of the slope is metres per second squared.
5) Acceleration
6) The symbol used for acceleration is [tex]a[/tex]
7) The relationship between velocity and time is [tex]v=gsin \theta t[/tex]
Explanation:
2)
The graph in the problem represents the velocity of the wheel as a function of the time.
As we can see from the graph, the velocity is increasing as the time passes. This means that the wheel is accelerating (its velocity is changing constantly)
3)
The slope of the graph represents the rate of change of the velocity.
Mathematically, it can be written as:
[tex]m=\frac{\Delta v}{\Delta t}[/tex]
where
m is the slope
[tex]\Delta v[/tex] is the change in velocity
[tex]\Delta t[/tex] is the time interval considered
As we see from the graph, the slope of the line is positive and constant: this means that the velocity is increasing at a constant rate.
4)
The unit of the slope can be determined starting by the units of the two variables involved.
On the y-axis, we have the velocity, which is measured in metre per second ([tex]m/s[/tex])
On the x-axis, we have the time, which is measured in seconds ([tex]s[/tex])
The slope is the ratio between these two quantities:
[tex]m=\frac{\Delta v}{\Delta t}[/tex]
Therefore, the units of the slope are
[tex]m=\frac{[m/s]}{[s]}=[m/s^2][/tex]
So, metres per second squared.
5)
The rate of change of velocity is also known as acceleration.
In fact, acceleration is defined as the ratio between the change in velocity and the change in time:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
By comparing with the formula of the slope in part 3), we see that the two equations are identical, therefore the acceleration corresponds to the slope of the graph.
6)
The symbol used to represent the acceleration is [tex]a[/tex]:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
7)
In any uniformly accelerated motion, the relationship between velocity and time is given by the following suvat equation:
[tex]v=u+at[/tex]
where
u is the initial velocity
v is the final velocity
a is the acceleration
t is the time
In this problem, the wheel starts from rest, so
u = 0
Also, for an object rolling down a ramp, the acceleration is given by
[tex]a=g sin \theta[/tex]
where g is the acceleration of gravity and [tex]\theta[/tex] is the angle of the ramp. Substituting, we find the final expression of the velocity:
[tex]v=gsin \theta t[/tex]
Learn more about acceleration:
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