Kinematics

Introduction

Before we can calculate forces or energy in the universe, we must master the art of describing motion itself. This is Kinematics. Consider a simple, everyday object: an ID card on a lanyard swinging from your fingers. To your eyes, it follows a predictable arc. But if you walk forward while swinging it, its path relative to a student sitting at a desk changes completely.

This brings us to the core axiom of IB Physics: Motion is absolute, but its description is completely relative. To quantify anything in kinematics, we must first establish a fixed coordinate framework known as a Frame of Reference. Once established, we track the position of an object treated as a single point mass.

Key Concepts

1. The Vector-Scalar Dichotomy

Physics carefully decouples how we measure space and time. We divide quantities into scalars (magnitude only) and vectors (magnitude and spatial direction).

• Distance (s) vs. Displacement (s): Distance is a scalar representing the total, winding ground covered. Displacement is a vector defining the direct, straight-line path from the start point to the end point, tracking both length and direction.
• Speed (v) vs. Velocity (v): Speed is the scalar rate of distance covered. Velocity is a vector tracking the precise rate of change of displacement over time.
• Acceleration (a): A vector quantity that measures the rate at which an object’s velocity changes over time. Because it is a vector, an object accelerates if it changes speed, changes direction, or both.

2. Motion Graphs (The Calculus of Tracking)

In IB Physics, understanding the relationships between displacement-time, velocity-time, and acceleration-time graphs is critical.

• Displacement–Time (s-t) Graphs: The gradient represents the instantaneous velocity.
• Velocity–Time (v-t) Graphs: The gradient represents the acceleration. The area enclosed under a velocity-time graph represents the total displacement of the object.
• Acceleration–Time (a-t) Graphs: The area enclosed under an acceleration-time graph represents the change in velocity.

3. The Equations of Motion (suvat)

When an object moves with constant, uniform acceleration along a straight line, its motion is governed by five structural algebraic relationships.

• v = u + at
• s = ((u + v) / 2) * t
• s = ut + 0.5 * a * t²
• s = vt - 0.5 * a * t²
• v² = u² + 2as

Where: u = initial velocity (m s⁻¹), v = final velocity (m s⁻¹), a = acceleration (m s⁻²), s = displacement (m), and t = time elapsed (s).

4. Fluid Resistance and Terminal Velocity

In a vacuum, all masses accelerate downward due to gravity at an identical, uniform rate (g = 9.81 m s⁻²). However, in the real world, objects experience fluid resistance (air drag).

As a falling object speeds up, the upward air resistance force increases. Eventually, the upward drag force perfectly equals the downward gravitational weight force. At this point, the net force is zero, acceleration drops to zero, and the object locks into a constant maximum speed known as Terminal Velocity.

Common Mistakes

• Confusing Negative Acceleration with Deceleration: A negative acceleration value does not automatically mean an object is slowing down. If an object is moving to the left (negative velocity) and experiences a negative acceleration, it is actually speeding up in that negative direction. Always look at the signs of both velocity and acceleration together.
• Using suvat Under Non-Uniform Acceleration: Students frequently try to use suvat formulas for situations where acceleration is changing (such as a skydiver experiencing air drag). Remember: if the acceleration is not perfectly constant, suvat fails. You must analyze the scenario using graphs instead.
• Misinterpreting Graph Gradients: Forgetting that a flat, horizontal line means entirely different things on different graphs. On an s-t graph, a flat line means the object is stationary. On a v-t graph, a flat line means the object is moving at a perfect, constant velocity.

Exam Tips

• Declare Your Frame Vector Signs Early: Before solving any multi-stage Paper 2 kinematics question, write down your vector convention at the top of the workspace page (e.g., “Upwards = Positive, Downwards = Negative”). If you launch a projectile upward, its initial velocity (u) is positive, but its acceleration (a) due to gravity must be entered as -9.81 m s⁻².
• The “Zero Velocity” Hint: Look closely for hidden conceptual values in word problems. Phrases like “starts from rest” mean u = 0. Phrases like “reaches maximum height” mean that at that exact apex moment, instantaneous vertical velocity v = 0.
• Be Exact with Units: IB Examiners scrutinize data presentation. Never write acceleration as “m/s²” or velocity as “m/s” on structural responses. Use standard IB index notation: m s⁻¹ for velocity and m s⁻² for acceleration.

Practice Questions

Question 1 (Multiple Choice)

A ball is thrown vertically upwards from the edge of a cliff, reaches its maximum height, and then falls past its launch point down to the base of the cliff. Air resistance is negligible. Which of the following correctly describes the acceleration of the ball throughout its entire flight path?

A. It decreases on the way up, is zero at the top, and increases on the way down. B. It is constant and directed downwards at all times. C. It is directed upwards on the way up and downwards on the way down. D. It is constant and directed upwards at all times.

Question 2 (Structured Paper 2 Style)

A laboratory trolley is initially travelling along a straight horizontal track at a constant velocity of 4.0 m s⁻¹. A braking mechanism is applied, causing the trolley to uniformly decelerate over a distance of 5.0 metres until it comes to a complete stop.

(a) Calculate the time taken for the trolley to come to rest. [2 marks]

(b) Determine the magnitude of the uniform deceleration. [2 marks]