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One and two dimensional motion
Formula
speed |
s = d/t -> 50 + 30 = 80 miles, 1+1 = 2h -> 80 miles/2h = 40 mph |
velocity |
v = ∆x/t |
average velocity |
v avg = ∆x/∆t = xf − xi/tf − ti -> 100 m in 10.61 s -> xf = 100 m, xi = 0 m, tf = 10.61 s, ti = 0 s -> v avg = 100 m - 0 m / 10.61 s - 0 s = 100/10.61 = 9.43 m/s |
Speed and Velocity
speed |
the distance traveled per unit of time. Speed is a scalar, a quantity that is described by magnitude alone. Constant speed refers to a fixed distance per unit of time. Average speed includes the total distance and total time. |
velocity |
the displacement of an object per unit of time. Since displacement includes a direction, so does velocity. Speed with direction. Velocity is a vector a quantity that has both magnitude and direction. |
vector |
a quantity that has both magnitude and direction |
reference frame |
the position from which an event is observed |
motion map |
an image that represents the position, velocity, and acceleration of an object at one-second intervals |
scalar |
a quantity that is described by magnitude alone |
Motion and reference frame |
All motion is relative. It depends on a reference frame. An object may appear to move faster or slower depending on the reference frame. |
average velocity |
The slope of a line changes when the velocity of an object changes -> The steeper the slope, the greater the velocity. The average velocity will be different than any of the other. Any point on the line will give only an instantaneous velocity. |
change in direction |
A change in direction is represented when the line on a position-time graph changes from a positive slope to a negative. slope or from a negative slope to a positive slope. A negative slope indicates an object moving towards the origin. A positive slope indicates an object moving away from the origin. |
No motion |
horizontal line - means object is not moving -> The object’s position does not change |
Motion |
Displayed in a vector ! |
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Horizontal motion example
Displacement during constant acceleration
Acceleration
positive acceleration |
an increase in velocity over time |
negative acceleration |
a decrease in velocity over time |
acceleration |
the rate at which velocity changes over time |
constant |
staying the same; unchanging |
Positive acceleration |
speeds up in the positive direction. slows down in the negative direction |
Negative acceleration |
slow down down in the positive direction. speeds up in the negative direction. |
Slope |
of the line on a velocity vs. time graph represents acceleration. Positive slope = acceleration, negative slope = negative acceleration |
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vectors
quadrant |
a quarter of the coordinate plane |
components |
the two parts of a vector that are perpendicular to each other |
resultant vector |
the sum of two or more vectors |
vector resolution |
the process by which the components of a vector are determined |
Properties of a vector |
A vector is a quantity that has both magnitude and direction. Examples of vectors: Displacement, velocity, acceleration. Vectors are drawn using an arrow |
Sign of a component
The sign of a component depends on the quadrant of the coordinate
system it is in.
Projectile Motion
projectile |
an object that is set in motion following a path in which the only force acting on it is gravity. |
inertia |
the natural tendency of objects to resist a change in motion |
projectile motion |
the curved motion that results from the combination of an object’s horizontal inertia and the force due to gravity pulling the object downward. I.e. A ball rolling of the table, A player shooting a jump shot -> Projectiles follow a parabolic path |
parabolic |
having the shape of a parabola |
vectors |
Vectors are used to describe motion in two dimensions. Vectors can be broken down into x and y components. The components of a vector are the two parts of a vector that are perpendicular to each other |
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