AP Physics 1 Review

General knowledge needed for the AP Physics 1 Exam

Displacement

How far an object ends up from its initial position, regardless of its total distance traveled.

Average velocity

Displacement divided by the time interval over which that displacement occured.

Instantaneous velocity

How fast an object is moving at a specific moment in time.

Distance from origin on a position-time graph

Vertical axis of position-time graph

Instantaneous speed from a curved position-time graph

Slope of the tangent line at that point (derivative)

Direction of motion of the object on a position-time graph

Sign of the slope of the position-time graph

Positive slope: Forwards

Negative slope: Backwards

Relation of position and slope to direction of motion from origin on a position-time graph

Positive slope and positive position: away from origin

Negative slope and positive position: towards origin (B until it crosses origin)

Positive slope and negative position: towards origin (D)

Negative slope and negative position: away from origin (B after it crosses origin)

Zero slope: Object is at rest

*This is direction of motion in relation to the origin (where it started). A positive slope still means the object is moving forward, and a negative slope still means it is moving backward, but depending on where it is will change whether it is moving towards or from where it started.

How fast an object is moving on a velocity-time graph

Vertical axis of velocity-time graph

Direction of motion of the object on a velocity-time graph

Sign of the velocity

Above the horizontal axis: Forwards

Below the horizontal axis: Backwards

Relation of position and slope to direction of motion from origin on a velocity-time graph

Positive velocity and positive position: away from origin

Negative velocity and positive position: towards origin (B until it crosses origin)

Positive velocity and negative position: towards origin (D)

Negative velocity and negative position: away from origin (B after it crosses origin)

Zero velocity: Object is at rest

*Important to remember you cannot figure out whether or not the object is moving towards or away from the origin without also knowing its position, only which direction the object is traveling in. This also means it is impossible to figure out how far away from the origin the object is without knowing its initial position.

Change in displacement on a velocity-time graph

Area between the velocity-time graph and the horizontal axis

Acceleration on a velocity-time graph

Slope of the velocity-time graph

Acceleration

Vector, how much an object’s speed changes in one second; change in velocity over time; change in position over time² (m/s²)

Velocity

Vector, how much an object’s displacement changes in one second; change in displacement over time (m/s)

Displacement

Vector, how far away the object is from the origin (m)

Distance

Scalar, how far the object traveled (m)

Speed

Scalar, change in distance over time (m/s)

Speeding Up/Slowing Down

Speeding up: Acceleration is in the direction of motion

Slowing down: Acceleration is opposite the direction of motion

Free Fall

Vertical Acceleration: -9.8 m/s² (or 10 m/s²)

Horizontal Acceleration: 0 m/s²

Special Equations for Displacement

When an object is moving at a constant speed: ∆x = vt + x₀

When an object starts at rest and speeds up, or when an object slows to a stop, its displacement is given by either:

∆x = ½ at²

∆x = v²/2a

Steps to solve an algebraic kinematics calculation

1) Define a positive direction, typically “away from the detector.” Label it and keep it consistent

2) Indicate what portion of the motion you are considering (start and end)

3) Fill out a chart including signs and units (motion chart)

a. Initial Velocity

b. Final Velocity

c. Displacement

d. Acceleration

e. Time

4) If three of the five variables are known, the problem is solvable; use the kinematics equations to solve.

a. v_f = v_o + at

b. ∆x = v_ot + ½ at²

c. v_f² = v_o² + 2a∆x

d. ∆x = ½ t(v_o + v_f)

Magnitude of an object’s velocity

Speed

Adding velocities in horizontal and vertical directions

Use the Pythagorean theorem to add perpendicular forces

Equilibrium

An object is in equilibrium if it is moving in a straight line at constant speed. This includes an object remaining at rest.

When an object is in equilibrium, forces on the object are balanced.

Newton’s Second Law

F=ma

An object’s acceleration is in the direction in which forces are unbalanced.

The net force is in the direction in which the forces are unbalanced.

The net force is in the direction of acceleration.