Cheatography

# One and two dimensional motion Cheat Sheet by anjuscha

One and two dimensional motion

### 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 !

### 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

### 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

### accele­ration ### Accele­ration example ### Displa­cement during constant accele­ration ### Formula ### Horizontal motion example ### Key concepts ### 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

### More ### 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 ### Horizontal ### Horizontal example ### continued 