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One and two dimensional motion Cheat Sheet by

One and two dimensional motion


s = d/t -> 50 + 30 = 80 miles, 1+1 = 2h -> 80 miles/2h = 40 mph
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

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.
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.
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
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
Displayed in a vector !

Key concepts

Horizontal motion example


Displa­cement during constant accele­ration

Accele­ration example



positive accele­ration
an increase in velocity over time
negative accele­ration
a decrease in velocity over time
the rate at which velocity changes over time
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.
of the line on a velocity vs. time graph represents accele­ration. Positive slope = accele­ration, negative slope = negative accele­ration


a quarter of the coordinate plane
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

an object that is set in motion following a path in which the only force acting on it is gravity.
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
having the shape of a parabola
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



Horizontal example




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