Motion describes a change of position over a specified time interval. The study of an objects motion, along with the related concept of force and energy, form the field of mechanics.
Mechanics can be studied from the perspective of how an object moves, (kinematics) or from why objects move and the role of force in creating motion. (dynamics).One-dimensional motion refers to motion along a single axis, like straight up or down.
To describe any motion requires a comparison to a fixed reference point. This fixed point is referred to as a reference point and the coordinate system around that point is the "frame of reference." Usually motion is relative to the stationary earth. Objects on the highway moving at 70 mph are doing 70 relative to the stationary ground they are moving along. You choose the frame of reference to describe the motion you observe. Inside a bus that is going 55 mph you can toss a tennis ball up and down. To you the ball has no horizontal velocity. To an observer on the side of the road that ball is moving up and down but also horizontally at 55 mph. Different frames of reference!
Frame of reference: a coordinate system that motions measured against. In physics our coordinate system is often a set of x or y axes.
When measuring motion we must distinguish between distance and displacement. Distance is the total range of motion that occurs while displacement is the change in position. If we walk a 100m circle the distance is 100m but the displacement is zero.
Displacement has a magnitude and a direction associated with it. If an object moves 100m north of its original location, the direction is needed to adequately describe that motion.
Any quantity, such as displacement that requires a magnitude and a direction to describe it, is a vector quantity. Quantities like speed (60 mph) don't require a direction. Other examples of quantities with no direction needed are temperature, mass, and volume. These are scalar quantities.
The most obvious aspect of an object motion is its rate of motion, the speed or velocity.
Average S = distance traveled
Elapsed time
Velocity and speed are used interchangeably but technically speed is scalar and velocity is a vector.
For most of our calculations we will assume velocity is constant and unchanging. To calculate velocity we must measure the change in displacement and divide by the elapsed time this displacement occurs.
A graph of the position of a moving object as a function of time yields a graph where the slope of the line represents the velocity. This makes sense when you remember that slope equals rise/run. The rise in this graph is displacement and the run is time, d/t = v.
Velocity can have a negative as well as a positive value. Since it is a vector quantity we can choose forward as positive and backwards as negative positions, thus making it possible for delta t to have a negative value. So we can see that the sign on velocity indicates direction.
If we calculate the velocity of an object and we decrease the delta t to an infinitesimally small increment, we have the velocity at a specific "instant" or instantaneous velocity.
Instantaneous velocity: When delta t approaches zero, the displacement during this time interval divided by that change in time.
In changing velocity, the slope will be curved on a graph of position vs. time. If we find the slope of a line drawn tangent to the curve at a single point we have the instantaneous velocity,
Acceleration is the rate of change of velocity where velocity is the rate of change of position. Since velocity is vector quantity acceleration involves a change of direction as well as a change in the magnitude of that velocity. Acceleration then can occur when an object changes direction and maintains the same speed. Newton noticed this when he observed the moon's orbit around the earth.
Instantaneous acceleration: as t approaches zero. The change in velocity divided by this increment of t yields the acceleration at that specific instant.
In the study of kinematics we use the basic equations for velocity and acceleration and manipulate them in such a fashion as to solve for a greater number of unknowns.
We can use V = d/t and solve for d to get d = Vt. Since the velocity here is constant the V we have is the average velocity. Another way to write average velocity is (Vf -Vi)/2
Thus d = (Vf -Vi)/2 x t This is the first kinematic equation.
We can take the acceleration equation a = (Vf -Vi)/t
Solve for Vf and we get Vf = Vi + at. This is the second kinematic equation
If we solve this for t it becomes t = (Vf -Vi)/a and we can plug this into the t of the very first equation.
d = (Vf +Vi)/2 x tbecomes d = (Vf -Vi)/2 x (Vf -Vi)/a
becomes d = (Vf -Vi)/2 x (Vf -Vi)/a d = (Vf2 - Vi2) / 2a
and solving for Vf2 = Vi2 + 2ad, this is the third equation.
The fourth involves plugging the value for Vi from the second equation into the first equation.
D = ((Vi + at) +Vi) /2 times t
this becomes
d = (2 Vi + at)/2 times t
or d = Vit + ½ at2, this is the fourth and final kinematic equation. The only remaining task is the application of these equation to describe how motion occurs.
