Kinematics is the branch of physics that describes motion without considering what causes it. Think of it as the "geometry of motion" - we're interested in how things move, not why they move.
In this tutorial, you'll master the fundamental concepts needed to ace your kinematics assignment and understand motion in the real world. Whether it's a car accelerating on a highway, a basketball arcing through the air, or a skydiver falling toward Earth, kinematics helps us predict and understand these motions mathematically.
Before we dive into equations, let's build a solid understanding of what each variable represents and how they relate to each other:
| Symbol | Quantity | Definition | Units (SI) | Real-World Example |
|---|---|---|---|---|
| d or x | Displacement | Change in position | meters (m) | Distance from home to school |
| v₀ | Initial velocity | Speed at start | m/s | Car's speed when light turns yellow |
| v | Final velocity | Speed at end | m/s | Car's speed when it stops |
| a | Acceleration | Rate of velocity change | m/s² | How quickly a car speeds up |
| t | Time | Duration of motion | seconds (s) | How long the trip takes |
| g | Gravity | Earth's acceleration | 9.8 m/s² | Why things fall down |
Speed is a scalar quantity (just a number) - it tells you how fast something is moving.
Velocity is a vector quantity - it tells you both speed AND direction.
Example: A car going 60 mph has a speed of 60 mph. A car going 60 mph north has a velocity of 60 mph north.
Many students confuse distance with displacement:
If you walk 3 blocks east then 3 blocks west, your distance is 6 blocks but your displacement is 0!
There are four fundamental kinematic equations. Each is useful in different situations:
Use when you know: initial velocity, acceleration, and time
This equation combines two ideas:
The ½ appears because acceleration gradually increases velocity over time, creating a triangular area under the velocity-time graph.
Use when you need final velocity
Use when time is unknown
Use for constant acceleration problems
A car starts from rest (v₀ = 0 m/s) at a stop sign and accelerates uniformly at 2 m/s² for 5 seconds. Let's find how far it travels.
Real-world context: This is about the length of 5-6 car lengths, showing why maintaining safe following distance is crucial!
When objects move vertically near Earth's surface, they experience a constant downward acceleration due to gravity: g = 9.8 m/s²
This value is the same for all objects, regardless of their mass! A feather and a hammer fall at the same rate in a vacuum (as demonstrated on the Moon by Apollo 15 astronauts).
When a ball is thrown straight up with initial velocity v₀:
Note: We use minus because gravity acts downward
In vertical motion problems:
This is why we write Y(t) = v₀t - ½gt² instead of Y(t) = v₀t + ½at²
A basketball is thrown upward with an initial velocity of 8 m/s. Let's analyze its motion:
At maximum height, velocity = 0. Using v = v₀ - gt:
Free fall occurs when an object moves under the influence of gravity alone. In true free fall:
Your assignment asks about a ball falling from a building of height = 6 × Day (in meters)
Given: A tennis ball is dropped from a 50-meter high cliff, g = 9.8 m/s²
Note: This example uses the same method you'll need for your building problem, just with different numbers!
In real life, air resistance significantly affects falling objects, especially at high speeds. Our calculations assume ideal conditions (no air resistance). Real objects would fall slightly slower due to air resistance, reaching a terminal velocity where drag force equals gravitational force.
| Location | Gravity (m/s²) | 90m Fall Time | Notes |
|---|---|---|---|
| Earth | 9.8 | 4.29 s | Standard conditions |
| Moon | 1.6 | 10.6 s | 1/6 Earth's gravity |
| Mars | 3.7 | 6.97 s | About 38% of Earth's |
| Jupiter | 24.8 | 2.69 s | Much stronger gravity! |
Try solving problems on your own first! The real learning happens when you work through the steps yourself. Use the practice problems below to build your skills.
Given: h = 90 m, g = 9.8 m/s², v₀ = 0 m/s (dropped)
Find: time to fall (t)
Solution:
Using h = ½gt²
90 = ½(9.8)t²
90 = 4.9t²
t² = 90/4.9 = 18.37
t = √18.37 = 4.29 s
Answer: t = 4.29 seconds
Try these problems using the same methods. Solutions are hidden - try them first!
A penny is dropped from the Empire State Building (380 m). How long does it take to hit the ground?
t = √(2h/g) = √(2×380/9.8) = √77.55 = 8.81 seconds
A baseball is thrown upward at 20 m/s. What is its position after 1.5 seconds?
Y(1.5) = 20(1.5) - ½(9.8)(1.5)² = 30 - 11.025 = 18.975 m
A car traveling at 25 m/s applies brakes with acceleration a = -5 m/s². How far does it travel in 3 seconds?
d = v₀t + ½at² = 25(3) + ½(-5)(3)² = 75 - 22.5 = 52.5 m
An object falls from height h = 6 × [your day]. Find the time and final velocity.
Remember: Use YOUR actual due date, not someone else's!
Before submitting your assignment, make sure you can answer these:
The normal force (N) is the push a surface gives back to an object resting against it. "Normal" is the math word for perpendicular: the normal force always points straight out of the surface, at 90° to it. It is not always straight up. It only points straight up when the surface is flat.
A surface pushes back only as hard as it needs to so the object does not sink into it. So the normal force is not a fixed number. It adjusts to match how hard the object is pressing into the surface.
The diagram below shows a block sitting still on a rough ramp. Three forces act on it: gravity, the normal force, and friction (which keeps it from sliding down). Notice the direction of each arrow. When you draw your own free-body diagram, start from the block and draw every force in the direction it acts on the block.
Solid arrows are real forces. Dashed arrows are the two pieces of gravity, not extra forces.
Gravity always pulls straight down, but on a ramp it is easier to think about it in two pieces:
Only forces that have a piece pointing into or out of the surface change the normal force. A push directed straight up the slope (parallel to the ramp) and friction (which always acts along the surface) have no piece perpendicular to the ramp, so they do not change N. Moving at a constant speed also does not change N.
If someone instead pushed horizontally or pressed down on the block, part of that push would point into the ramp and N would be larger.
A 10 kg box (W = mg = 98 N) sits on a flat floor. Use the slider to press down on it with your hand (positive) or pull up on it (negative), and watch how the floor's normal force responds.
A qualitative question needs no numbers, but a clear reason is required.
Before submitting, ensure you have:
For those interested in the mathematical foundation:
This is why the position equation has a t² term - it's from integrating acceleration twice!
Understanding kinematics opens doors to exciting careers:
Kinematics is the foundation of understanding motion in our universe. From the smallest particles to the largest celestial bodies, everything follows these same fundamental principles. By mastering these concepts, you're not just completing an assignment - you're gaining tools to understand and predict the physical world around you.
Remember: Physics is about understanding patterns and relationships. Once you see how position, velocity, and acceleration connect, you'll find these problems become much more intuitive. Keep practicing, stay curious, and don't hesitate to work through multiple examples!