UPCAT Physics — Kinematics & Speed, Velocity, AccelerationStudy Notes
Full study notes for Kinematics & Speed, Velocity, Acceleration — built specifically for the UPCAT 2026. These notes cover every concept, definition, formula, and worked example you need for the Physics subtest of the UPCAT, structured in the order University of the Philippines typically tests them.
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 - Study notes
Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. In this chapter, we will explore the fundamental concepts of speed, velocity, and acceleration - the building blocks for understanding how objects move in our everyday world. From a jeepney traveling down EDSA to a basketball player shooting hoops, these concepts help us describe and predict motion mathematically.
Summary
Kinematics describes motion using three fundamental quantities: speed (how fast), velocity (how fast with direction), and acceleration (how velocity changes). Speed and distance are scalars with magnitude only, while velocity and displacement are vectors with both magnitude and direction. Acceleration occurs when velocity changes in magnitude or direction. The kinematic equations help us solve motion problems for constant acceleration, and free fall is a special case where gravity provides constant acceleration of 9.8 m/s² downward. Understanding these concepts is essential for analyzing motion in everyday situations and forms the foundation for more advanced physics topics.
Sections
Motion is everywhere around us - from the tricycles weaving through Manila traffic to the waves crashing on Boracay's shores. Kinematics helps us describe this motion using mathematical relationships. The key to understanding kinematics is distinguishing between distance and displacement, speed and velocity, and understanding how these quantities change over time. When we study motion, we need a reference point or frame of reference - imagine describing the motion of a passenger inside a moving bus versus someone watching from the sidewalk. The description of motion depends on your perspective!
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Understanding Motion and Kinematics
Examples
- A jeepney traveling from Quezon City to Makati follows a path with specific positions at different times
- A student walking from classroom to canteen - we can measure total distance walked vs. direct displacement
Key Points
- Kinematics describes motion without considering forces
- Motion is relative to the observer's frame of reference
- Position, distance, and displacement are fundamental concepts
- Time is the independent variable in motion equations
Speed tells us how fast an object is moving. It's a scalar quantity, meaning it only has magnitude (size) but no direction. Think of the speedometer in a car - it shows 60 km/h but doesn't tell you whether you're going north or south. Average speed is calculated by dividing the total distance traveled by the total time taken. For example, if a bus travels 100 kilometers in 2 hours, its average speed is 50 km/h. Instantaneous speed is the speed at any specific moment - like when you glance at a speedometer and see exactly 45 km/h. The SI unit for speed is meters per second (m/s), but we commonly use kilometers per hour (km/h) for vehicles.
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Speed: How Fast Objects Move
Examples
- A tricycle travels 15 km in 30 minutes, so average speed = 15 km ÷ 0.5 h = 30 km/h
- An athlete runs 400m in 50 seconds, so average speed = 400m ÷ 50s = 8 m/s
Key Points
- Speed is a scalar quantity (magnitude only, no direction)
- Average speed = total distance ÷ total time
- Instantaneous speed is speed at a specific moment
- SI unit: m/s; common unit: km/h
Velocity is speed with a direction - it's a vector quantity. While speed only tells us 'how fast,' velocity tells us 'how fast and which way.' If two jeepneys are both traveling at 40 km/h but one is heading north and the other south, they have the same speed but different velocities. Average velocity is displacement divided by time. Displacement is the shortest straight-line distance from starting point to ending point, with direction. This is different from total distance traveled. For instance, if you walk around a basketball court and return to your starting position, your displacement is zero even though you traveled a considerable distance.
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Velocity: Speed with Direction
Examples
- A student walks 200m east in 40 seconds: velocity = 200m east ÷ 40s = 5 m/s east
- If you drive from Manila to Baguio and back, your total distance is about 500km, but displacement is zero
Key Points
- Velocity is a vector quantity (has both magnitude and direction)
- Average velocity = displacement ÷ time
- Displacement is different from distance
- Velocity can be negative (indicating opposite direction)
Acceleration describes how quickly velocity changes over time. It's also a vector quantity, so it has both magnitude and direction. When a jeepney speeds up from rest to 50 km/h, it's accelerating. When it slows down (decelerates), it's also accelerating, but in the opposite direction to its motion. Average acceleration equals the change in velocity divided by the time taken. If a car's velocity changes from 20 m/s to 30 m/s in 5 seconds, its acceleration is (30-20) ÷ 5 = 2 m/s². The unit m/s² means 'meters per second per second' - the velocity changes by 2 m/s every second.
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Acceleration: How Velocity Changes
Examples
- A motorcycle accelerates from 0 to 20 m/s in 4 seconds: a = (20-0) ÷ 4 = 5 m/s²
- A basketball thrown upward decelerates due to gravity at -9.8 m/s²
Key Points
- Acceleration is the rate of change of velocity
- Acceleration is a vector quantity
- Formula: a = (v_final - v_initial) ÷ time
- SI unit: m/s² (meters per second squared)
Kinematic equations help us solve motion problems mathematically. The most important equations relate position, velocity, acceleration, and time. For constant acceleration, we use: v = v₀ + at (final velocity), s = v₀t + ½at² (displacement), v² = v₀² + 2as (velocity-displacement relationship), and s = (v₀ + v)t ÷ 2 (average velocity method). These equations assume constant acceleration. When solving problems, identify what's given, what's asked, choose the appropriate equation, substitute values, and solve. Always include proper units in your answer and check if the result makes physical sense.
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Kinematic Equations and Problem Solving
Examples
- A ball is thrown upward with initial velocity 15 m/s. Using v = v₀ + at, after 1 second: v = 15 + (-9.8)(1) = 5.2 m/s
- A car accelerates at 3 m/s² for 6 seconds from rest. Distance traveled: s = 0 + ½(3)(6²) = 54 m
Key Points
- Kinematic equations work for constant acceleration only
- Four main equations relate v, v₀, a, t, and s
- Problem-solving requires identifying knowns and unknowns
- Always check units and reasonableness of answers
Free fall is motion under gravity alone, without air resistance. Near Earth's surface, all objects in free fall accelerate downward at g = 9.8 m/s² regardless of their mass. This seems counterintuitive because a feather falls slower than a rock in air, but that's due to air resistance. In a vacuum, they fall at the same rate. When an object is thrown upward, it slows down, stops momentarily at maximum height, then falls back down. The time to reach maximum height equals the time to fall back to the throwing point. Free fall motion follows the same kinematic equations, with acceleration = -g (negative because we typically consider upward as positive).
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Free Fall and Gravity
Examples
- A stone dropped from Banaue Rice Terraces viewpoint falls with a = 9.8 m/s²
- A basketball thrown upward takes 2 seconds to reach maximum height, then 2 seconds to return
Key Points
- Free fall acceleration g = 9.8 m/s² downward
- All objects fall at the same rate in vacuum
- Upward motion: object slows down until it stops
- Downward motion: object speeds up
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