Kinematics Solver

Master motion analysis with interactive calculations and visual animations

Understanding Kinematics

Kinematics is the branch of physics that describes motion without considering the forces that cause it. Understanding motion requires analyzing the relationships between five key variables: initial velocity (u), final velocity (v), acceleration (a), displacement (s), and time (t).

The Five Kinematic Variables:

  • Initial velocity (u): How fast an object is moving when we start observing it
  • Final velocity (v): How fast the object is moving at the end of our observation
  • Acceleration (a): How quickly the velocity changes over time
  • Displacement (s): The total change in position from start to finish
  • Time (t): How long the motion takes to occur

How It Works: If you know any three of these variables, you can calculate the remaining two using kinematic equations. This is because motion follows predictable mathematical patterns when acceleration is constant.

Projectile Motion: When objects move through the air under gravity's influence, we analyze their motion in two dimensions - horizontal and vertical components working independently.

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Practice Questions

Test your understanding with these kinematics problems. Click on the best answer for each question.

1. A car accelerates from rest at 3 m/s² for 5 seconds. What is its final velocity?
Correct answer: 15 m/s
Using v = u + at: v = 0 + (3)(5) = 15 m/s. Starting from rest means u = 0.
2. Which kinematic equation should you use when time is unknown but displacement, initial velocity, final velocity, and acceleration are given?
Correct answer: v² = u² + 2as
This equation doesn't contain time (t), making it perfect when time is unknown but other variables are given.
3. A ball is thrown horizontally from a 20m high building. What determines how long it takes to hit the ground?
Correct answer: Height and gravity only
Vertical motion is independent of horizontal motion. Time = √(2h/g), depending only on height and gravity.
4. For maximum range in projectile motion on level ground, what launch angle should be used?
Correct answer: 45°
At 45°, sin(2θ) = sin(90°) = 1, which maximizes the range formula R = u²sin(2θ)/g.
5. A stone is dropped from rest. After 3 seconds, what is its displacement? (g = 9.8 m/s²)
Correct answer: 44.1 m
Using s = ut + ½at²: s = 0 + ½(9.8)(3²) = ½(9.8)(9) = 44.1 m. Initial velocity u = 0 for dropped objects.
6. In projectile motion, what happens to the horizontal velocity component throughout the flight?
Correct answer: Remains constant
No horizontal forces act on the projectile (ignoring air resistance), so horizontal velocity stays constant throughout flight.
7. A car traveling at 20 m/s brakes with constant deceleration and stops in 4 seconds. What was its acceleration?
Correct answer: -5 m/s²
Using a = (v - u)/t: a = (0 - 20)/4 = -5 m/s². Negative because it's deceleration (slowing down).

Kinematics Glossary

Click on any term below to see its definition and understand key concepts.