One and two dimensional motion
s = d/t -> 50 + 30 = 80 miles, 1+1 = 2h -> 80 miles/2h = 40 mph
v = ∆x/t
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
the position from which an event is observed
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.
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.
horizontal line - means object is not moving -> The object’s position does not change
Displayed in a vector !
Horizontal motion example
Displacement during constant acceleration
an increase in velocity over time
a decrease in velocity over time
the rate at which velocity changes over time
staying the same; unchanging
speeds up in the positive direction. slows down in the negative direction
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
the sum of two or more vectors
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.
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
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