1-D Kinematics

Kinematics

study of things in motion, need to describe how things are moving

• use models to simplify problems

Motion

everything in universe is moving

• need a reference frame to solve problems

• x axis → 1 direction = 1 motion

Relative Motion

the motion of an object as observed from a particular reference frame, often involving multiple moving objects.

Motion Diagram

a visual representation of an object's motion, showing its position at various time intervals, typically using arrows to indicate direction and displacement.

Vectors

any quantity w/ a magnitude & direction

• speed X a vector → only magnitude

• magnitude seen as an absolute value

Velocity

a vector quantity that represents the rate of change of an object's position, including both speed and direction.

Quantities

time → t (s)

• time intervals → delta t = tf-ti

Position

location w/ respect to a frame of reference

Displacement

how far we move & in what direction (+/-) → change in position

• vector (d w/ >)

• d = xf-xi

Distance

magnitude of the displacement, absolute value

• X a vector, losing direction by being an absolute value

• just d

Path Length

how far something actually travels

• cursive l = sign

• includes all the details of motion

Position vs Time Graph

A graphical representation showing the relationship between an object's position and the elapsed time. The slope of the graph indicates the object's velocity.

• slope = displacement (delta x)/elapsed time (delta t)

• slope = velocity!

Acceleration

the rate of change of velocity over time, indicating how quickly an object's speed or direction changes.

• accelerate by inc/dec speed or direction

To define the position of an object in a plane, you need to measure __________.  

the object’s distance from a reference point & its angle measured from a reference line

2 Parts of an object on a plane

• both of these measurements are necessary to define an exact position.

  • its distance from a reference point

  • its angle measured from a reference line

What happens if you only know the object’s distance from a reference point?

X know everything about its position

• could be to the right of the reference point, or above, or below, etc.

What happens if you only know the angle that the object has from a reference line?

X define exact location, X know everything about that object’s position

• object could be any distance away from the origin

How is an object’s speed defined?

measure of a changing position

• alone X be used to define the position of an object

If an object’s acceleration vector points in the same direction as its instantaneous velocity vector then you can conclude __________.  

object must be speeding up

• for the acceleration to point in the same direction of the velocity, the change in velocity vector must have the same sign (+ or -) as the acceleration

• ^^ only occurs when the final speed is greater than the initial speed = speed up

T/F: A hammer that’s tossed upqard by an astronaut on the moon (that has no atmosphere) is in free fall.

True, it is in free fall because the only force acting on it is gravity.

What is g?

The acceleration due to gravity, approximately $9.8 \, m/s^2$ near the Earth's surface.

• moving down/naturally = +9.8 m/s²

• moving up = -9.8 m/s²

If an object’s acceleration vector points in the opposite direction of the instantaneous velocity vector, then you can conclude __________.  

object must be slowing down

Instead of dropping a ball, you throw a ball directly downward. After releasing the ball, what is the magnitude of its acceleration?  

9.8 m/s²

• is an object in free fall, only force acting on it is gravity

When you throw a ball directly upward, what is true about its acceleration?  

The ball’s acceleration is always directed downward due to gravity

When you drop a ball, what is true about its motion?  

it falls & inc speed at a rate of 9.8 m/s every second

A ball is dropped off of a tall building and falls for 6 seconds before landing on the ground. Consider how far the ball falls in its first 3 seconds of free fall (from t = 0 s to t = 3 s) compared to how far it falls in its next 3 seconds (from t = 3 s to t = 6 s).  

The ball falls farther in the second interval due to increasing velocity, covering a greater distance as time progresses.