Physics H Kinematics Notes

Scalar

A quantity that has magnitude (size/amount, including units) ONLY — no direction

Vector

A quantity that has BOTH magnitude and direction

Magnitude

The size or amount of a quantity, including units

How are vectors represented

By arrows — the length of the arrow = magnitude, the direction it points = direction

Sign convention: North/Up

Positive (+)

Sign convention: South/Down

Negative (−)

Sign convention: East/Right

Positive (+)

Sign convention: West/Left

Negative (−)

Adding vectors in the SAME direction

Simply add their magnitudes together (e.g., 46.5 m E + 20 m E = 66.5 m E)

Adding vectors in OPPOSITE directions

Add them, but treat one as negative (e.g., 46.5 m E + (−20 m W) = 26.5 m E)

Non-collinear (perpendicular) vectors

Use the Pythagorean theorem (a² + b² = c²) to find the resultant

Resultant

The hypotenuse/result of combining two perpendicular vectors — where you end up relative to where you started

Distance

Scalar quantity; the TOTAL path traveled; can only be zero if you don't move

Displacement

Vector quantity; the CHANGE in position (final − initial); can be zero after a round trip

Displacement formula

Δx = x_f − x_i

Round trip: distance vs displacement

Distance is greater than zero (path was walked), but displacement is zero (start = finish)

Speed

Scalar quantity that tells how fast an object is moving

Average speed formula

Total distance ÷ total time

Units of speed

meters/second (m/s)

Average speed vs instantaneous speed

Average = total distance ÷ total time (whole trip summary); Instantaneous = speed at one instant (what a speedometer shows)

Velocity

Vector quantity — the rate at which an object changes its position (includes direction)

Average velocity formula

Displacement ÷ total time

Units of velocity

meters/second (m/s)

Negative velocity means

The object is moving left (or in the negative direction)

Positive velocity means

The object is moving right (or in the positive direction)

Why can speed and velocity differ for the same trip

Speed depends on total distance traveled; velocity depends on displacement — a round trip has distance but zero displacement, so average velocity = 0 while average speed does not

Acceleration

Vector quantity — the rate at which an object changes its velocity

Average acceleration formula

a = Δvelocity / time = (v_f − v_i) / t

Units of acceleration

meters/second/second (m/s²)

Rule for direction of acceleration

If an object is SLOWING DOWN, acceleration is opposite the direction of motion. If an object is SPEEDING UP, acceleration is in the same direction as motion.

Positive acceleration occurs when

The object speeds up while moving in the + direction, OR slows down while moving in the − direction

Negative acceleration occurs when

The object slows down while moving in the + direction, OR speeds up while moving in the − direction

Uniform acceleration

When an object's velocity increases at a constant rate (the rate of acceleration doesn't change)

Acceleration due to gravity (g)

g = −9.8 m/s² (a uniform acceleration)

Free fall

Motion where gravity is the ONLY force acting on the object (air resistance neglected); all objects fall with the same constant acceleration

Free-fall formula for velocity

v = gt (only valid when dropped from rest)

Free-fall formula for height/displacement

h = ½gt² (only valid when dropped from rest)

Hammer vs. feather demonstration (Apollo 15)

In a vacuum (no air resistance), a hammer and feather fall and land at the same time — proving all objects accelerate equally under gravity regardless of mass