Physics Extra Credit

By: Grace Graber

Definitions

Velocity

An origin and location of something. Slope of a line of a position vs. time graph means Velocity.

Position

A variable of location with an origin.

Delta

The change of something.

Acceleration

The rate of change of velocity per unit of time.

Equations

Acceleration

A = V final - V intial/Time

Velocity

V = Distance/Time

Slope

Rise/Run

Pictures of the Equations

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Examples

Example 1

If a car takes 20 seconds to travel from 20m to 84m, what the velocity of the car?

84 - 20 = 64m

64/20 = 3.2

V = 3.2 m/s

Example 2

If two cars are racing and Car A has 3 m/s and Car B has 4 m/s. How much time does it take for the cars to have acceleration of 8 m/s2?

8 = 4-3/t = 8 * t = 1/t * t

8t/8 = 1/8

t = 0.125s

Graphs

Velocity vs. Time Graphs

The velocity vs. time graph has velocity on the y-axis and time on the x-axis.

Calculating Displacement

A velocity vs. time graph also can be used to find the object’s displacement. Displacement equals the velocity multiplied by the time, Delta*x = vt. The area of the triangle is equal to its length times its height.

Velocity vs. time graphs of Accelerated Motion

The Velocity vs. Time Graph

If an object is accelerating, it is easier to work with the velocity vs. time graph than it is to work with the position vs. time graph. The velocity vs. time graph is the best tool for understanding acceleration. It clearly shows how the velocity of an object changes with time.

Constant Acceleration

Make sure not to confuse constant velocity with constant acceleration. As long as it’s moving in one direction, an object at constant speed has zero acceleration. Constant velocity means an object’s position changes by the same amount each second. Constant acceleration means an object’s velocity changes by the same amount each second.

Calculating Acceleration

The slope of a velocity vs. time graph represents the acceleration of the object. Note that there is non-zero acceleration any time the velocity vs. time graph is not perfectly horizontal.

Calculating acceleration from the Velocity vs. Time Graph

Slope

The slope of a graph is equal to the ratio of rise to run. On the velocity vs. time graph, the rise and run have special meanings. The rise is the amount the velocity changes. The run is the amount the time changes.

Acceleration and Slope

Acceleration is the change in velocity over the change in time. This is exactly the same as the rise over run for the velocity vs. time graph. The slope of the velocity vs. time graph is equal to its acceleration.

Make a little Triangle to get the Slope

To determine the slope of the velocity vs. time graph, take the change in velocity and divide by the change in time. It is helpful to draw a triangle on the graph to identify the rise and run. The rise is the height of the triangle. The run is the length of the base of the triangle.

Displacement on an Accelerated-Motion Graph

Displacement

Area = ½(2 s) * (2m/s) = 2 m

Example

½ * t*v

Direction on Motion Graphs

A positive displacement and positive velocity occurs when the car moves away from the sensor. The opposite is true for motion toward the sensor.

Newton’s First Law of Motion

Force

A push, pull, or other action that has the ability to change motion.

Forces, Mass, Inertia

Newton's First Law

An object at rest will stay at rest and an object in motion will stay in motion with the same velocity unless acted on by an outside force.

Inertia

The property of an object that resists changes in motion.

Mass

It's measured in kilograms (kg).

Units of Force

Pounds

A unit of force commonly used in the United States.

Newton

The SI unit of force.

1 Pound

4.448 newtons

The Net Force

Net Force

The total of all forces acting on an object.
In physics, the term holds up means, "applies a force."

Applications of Newton’s first law

  • Seat belts and airbags
  • Cup holders
  • The tablecloth trick

Newton's Second law

Newton's Second Law

Relates to the net force acting on an object to its mass and acceleration.

Equation

A = F/M

Acceleration = Force/Mass

Force causes acceleration, and mass resists acceleration.

Three Forms of the Second Law

  1. A = F/m - acceleration (a) - force (F) and mass (m)
  2. F = ma - force(F) - mass (m) and acceleration (a)
  3. M = F/a - mass (m) - force (F) and acceleration (a)

Gravity and Free Fall

Free Fall

The acceleration of a falling object due to Earth's gravity.

The Acceleration of Gravity

The acceleration of an object due to Earth's gravity that is equal to 9.8 m/s/s and represented by g.

Free Fall Velocity Equation

V = gt - velocity (m/s) = Acceleration due to gravity (m/s/s) * Time (s)

Average Velocity Equation

V avg = Vf + Vi/2 - Average Velocity (m/s) = Final Velocity + Initial Velocity (m/s) / 2

Calculating Distance

d = V avg * t - Distance (m) = Average Velocity (m/s) * Time (s)

Gravity and weight

Weight

The force of gravity acting on and object.

Weight Equation

F w = mg - Weight or force of gravity (N) = Mass (kg) * Strength of Gravity (9.8 N/kg)

Air Resistance

Air Resistance

A force that acts against the force of gravity on an object in free fall.

Terminal Velocity

Terminal Velocity

The maximum velocity reached by an object in free fall in which the forces of gravity and air resistance are equal.
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