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One and two dimensional motion
Speed and Velocityspeed | 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 ! |
Formulaspeed | 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 |
| | Accelerationpositive 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 |
Displacement during constant acceleration
Horizontal motion example
| | vectorsquadrant | 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 componentThe sign of a component depends on the quadrant of the coordinate
system it is in. Projectile Motionprojectile | 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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