UPCAT Physics — Kinematics & Speed, Velocity, AccelerationCheat Sheet
Cheat sheet for UPCAT Physics — Kinematics & Speed, Velocity, Acceleration. Compact, printable, and organised around the concepts University of the Philippines tests most frequently in the UPCAT 2026. Perfect for the week before exam day.
Exam context
On the UPCAT 2026, the Physics subtest carries a "Core" weight in University of the Philippines's pattern. Kinematics & Speed, Velocity, Acceleration lands at position 2nd out of 6 in the standard review order. Target score is UPG ≤ 2.2 typical, and roughly 20 items come from Physics on a typical UPCAT paper.
Kinematics & Speed, Velocity, Acceleration - Cheat sheet
Your last-minute revision companion for Kinematics - all formulas, definitions, and key concepts for motion problems in one place.
Sections
Formulas
Formula
Average Speed = Distance / Time
Meaning
Speed (m/s), Distance (m), Time (s)
Watch Out
Don't confuse distance with displacement - speed uses total path length
When To Use
When finding how fast an object moves regardless of direction
Formula
Average Velocity = Displacement / Time
Meaning
Velocity (m/s), Displacement (m), Time (s)
Watch Out
Velocity can be negative if moving in opposite direction to positive axis
When To Use
When direction matters - finding rate of change of position
Formula
Average Acceleration = (v_f - v_i) / t
Meaning
a (m/s²), v_f (final velocity), v_i (initial velocity), t (time)
Watch Out
Negative acceleration doesn't always mean slowing down - check direction
When To Use
When velocity is changing uniformly over time
Common Values
Value
9.8 m/s² (or 10 m/s² approximation)
Symbol
g
Quantity
Acceleration due to gravity
Section Title
Basic Motion Quantities
Important Facts
- Speed is always positive; velocity can be positive or negative
- Instantaneous speed equals magnitude of instantaneous velocity
- Average speed ≠ magnitude of average velocity (unless motion is in one direction)
- SI base unit for speed and velocity: m/s
- SI base unit for acceleration: m/s²
Key Definitions
Term
Speed
Example
Car travels 60 km/h regardless of direction
Definition
Rate of motion; scalar quantity with magnitude only
Term
Velocity
Example
Car travels 60 km/h eastward
Definition
Rate of change of displacement; vector quantity with magnitude and direction
Term
Acceleration
Example
Car speeds up by 5 m/s every second
Definition
Rate of change of velocity; vector quantity
Term
Displacement
Example
Move 10m east, then 6m west = 4m east displacement
Definition
Change in position from start to end point; vector quantity
Diagrams To Know
- Position-time graphs
- Velocity-time graphs
- Acceleration-time graphs
- Vector diagrams for displacement and velocity
Formulas
Formula
v_f = v_i + at
Meaning
Final velocity, initial velocity, acceleration, time
Watch Out
Time must be positive; check if acceleration opposes initial velocity
When To Use
When you need final velocity and don't care about displacement
Formula
d = v_i×t + (1/2)at²
Meaning
Displacement, initial velocity, time, acceleration
Watch Out
Don't forget the 1/2 factor in the acceleration term
When To Use
When finding displacement with known initial conditions
Formula
v_f² = v_i² + 2ad
Meaning
Final velocity squared, initial velocity squared, acceleration, displacement
Watch Out
Remember to take square root at the end; watch signs for direction
When To Use
When time is unknown but you have velocities and displacement
Formula
d = ((v_i + v_f)/2) × t
Meaning
Displacement equals average velocity times time
Watch Out
Only works for constant acceleration - average velocity formula
When To Use
When you have initial and final velocities and time
Section Title
Kinematic Equations (Uniformly Accelerated Motion)
Important Facts
- All kinematic equations apply only to constant acceleration
- Choose equation based on which quantity you're NOT given
- At highest point of projectile motion: vertical velocity = 0
- Time to reach maximum height = time to fall back down (symmetry)
Key Definitions
Term
Uniform Motion
Example
Car on cruise control at 80 km/h
Definition
Motion with constant velocity (zero acceleration)
Term
Uniformly Accelerated Motion
Example
Ball dropping under gravity only
Definition
Motion with constant acceleration
Term
Free Fall
Example
Dropped ball ignoring air resistance
Definition
Motion under gravity alone with acceleration g = 9.8 m/s²
Diagrams To Know
- Free fall motion diagrams
- Kinematic graph interpretations
- Vector addition diagrams
Reactions Or Equations
Note
Sign depends on chosen coordinate system
Equation
For free fall: a = -g = -9.8 m/s² (if up is positive)
Conditions
Near Earth's surface, ignoring air resistance
Formulas
Formula
x = v₀ₓ × t (horizontal)
Meaning
Horizontal displacement, initial horizontal velocity, time
Watch Out
Horizontal velocity remains constant throughout flight
When To Use
Finding horizontal distance traveled (no horizontal acceleration)
Formula
y = v₀ᵧt - (1/2)gt² (vertical)
Meaning
Vertical displacement, initial vertical velocity, time, gravity
Watch Out
Use negative g if upward is positive; check coordinate system
When To Use
Finding vertical position at any time
Formula
vᵧ = v₀ᵧ - gt (vertical velocity)
Meaning
Vertical velocity component at time t
Watch Out
Becomes zero at maximum height, negative on way down
When To Use
Finding vertical velocity at any instant
Formula
Range = (v₀² sin(2θ))/g
Meaning
Maximum horizontal distance for projectile launched at angle θ
Watch Out
Maximum range occurs at 45° launch angle
When To Use
Finding range for projectile launched and landing at same height
Section Title
Projectile Motion
Important Facts
- Horizontal and vertical motions are independent
- Horizontal velocity stays constant (no air resistance)
- Vertical motion is uniformly accelerated with a = -g
- Time of flight depends only on vertical motion
- Maximum range achieved at 45° launch angle
Key Definitions
Term
Projectile
Example
Basketball after leaving player's hands
Definition
Object moving under influence of gravity alone after initial launch
Term
Trajectory
Example
Arc of a soccer ball kicked into goal
Definition
Curved path followed by a projectile (parabolic shape)
Term
Range
Example
How far a cannon ball travels horizontally
Definition
Horizontal distance traveled by projectile
Diagrams To Know
- Projectile trajectory parabola
- Velocity vector diagrams at different points
- Component vector breakdown
Reactions Or Equations
Note
Break initial velocity into horizontal and vertical components
Equation
v₀ₓ = v₀ cos(θ), v₀ᵧ = v₀ sin(θ)
Conditions
For projectile launched at angle θ to horizontal
Formulas
Formula
v = 2πr/T
Meaning
Speed, radius, period (time for one revolution)
Watch Out
This gives magnitude only; velocity direction constantly changes
When To Use
Finding speed in uniform circular motion
Formula
a_c = v²/r = 4π²r/T²
Meaning
Centripetal acceleration, speed, radius, period
Watch Out
Acceleration is always toward center, perpendicular to velocity
When To Use
Finding acceleration toward center in circular motion
Formula
f = 1/T
Meaning
Frequency (revolutions per second), period
Watch Out
Frequency in Hz (s⁻¹), period in seconds
When To Use
Converting between frequency and period
Section Title
Circular Motion
Important Facts
- Speed constant but velocity changes (direction changes)
- Centripetal acceleration always points toward center
- No tangential acceleration in uniform circular motion
- Centripetal force required to maintain circular motion
Key Definitions
Term
Uniform Circular Motion
Example
Satellite orbiting Earth at constant altitude
Definition
Motion in circle at constant speed with changing direction
Term
Centripetal Acceleration
Example
Force that keeps car turning around a curve
Definition
Acceleration directed toward center of circular path
Term
Period
Example
Earth's period around sun is 1 year
Definition
Time required for one complete revolution
Diagrams To Know
- Circular motion velocity vectors
- Centripetal acceleration direction
- Free body diagrams for circular motion
Must Remember
- Speed = distance/time (scalar), Velocity = displacement/time (vector)
- Acceleration = change in velocity/time (can be negative)
- Four kinematic equations for constant acceleration only
- Free fall acceleration g = 9.8 m/s² downward
- Projectile motion: horizontal velocity constant, vertical accelerated by gravity
- At maximum height of projectile: vertical velocity = 0
- Uniform circular motion: constant speed, centripetal acceleration = v²/r toward center
- Choose kinematic equation based on which variable is unknown/not given
- Vector quantities have magnitude AND direction; scalars have magnitude only
- Average velocity can be zero even if average speed is not zero
Last Minute Tips
- Draw diagrams for projectile motion - separate horizontal and vertical components
- Check units in your final answer - speed (m/s), acceleration (m/s²)
- For free fall problems, decide coordinate system first (up positive or negative)
- In circular motion, remember acceleration points toward center, not in direction of motion
- When velocity and acceleration are in opposite directions, object is slowing down
Comparison Tables
Rows
Values
- Scalar
- Vector
- Vector
Property
Type
Values
- No
- Yes
- Yes
Property
Direction
Values
- No
- Yes
- Yes
Property
Can be negative
Values
- m/s
- m/s
- m/s²
Property
SI Unit
Values
- Rate of motion
- Rate of displacement
- Rate of velocity change
Property
Measures
Columns
- Property
- Speed
- Velocity
- Acceleration
Table Title
Speed vs Velocity vs Acceleration
Rows
Values
- Scalar
- Vector
Property
Type
Values
- Yes
- No
Property
Path dependent
Values
- Only if no motion
- Yes, if return to start
Property
Can be zero
Values
- Yes
- No
Property
Always positive
Values
- Total path walked
- Straight line start to end
Property
Example
Columns
- Property
- Distance
- Displacement
Table Title
Distance vs Displacement
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