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Kinematics

CSCA Kinematics study guide organized around the publicly available CSCA syllabus. Practice Physics questions on aicsca.com.

Before planning this topic, check the CSCA Exam Guide 2026 for exam dates, registration, fees, and subject requirements.

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This study guide is organized around the publicly available CSCA syllabus for international undergraduate applicants.

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International students preparing for CSCA Math, Physics, Chemistry, or Chinese exams.

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Kinematics

1. Core Concepts & Models

Kinematics is the foundation of mechanics. It describes **how** objects move (position, velocity over time) without considering **why** (forces).

* **Particle Model**: An idealized object with mass but no size/shape. This simplification is valid when the object's size is negligible compared to the travel distance.

2. Three Core Physical Quantities

For the CSCA exam, you must strictly distinguish between Scalars and Vectors.

* **Displacement ($\vec{x}$ or $\vec{s}$)**:

* **Definition**: The vector pointing from the initial position to the final position.

* **Vs. Distance**: Distance is the total length of the path traveled. **Displacement depends only on start and end points; Distance depends on the path.**

*

* **Velocity ($\vec{v}$)**:

* **Definition**: Rate of change of displacement ($v = \frac{dx}{dt}$).

* **Vs. Speed**: Speed is a scalar (Rate of change of distance).

* **Acceleration ($\vec{a}$)**:

* **Definition**: Rate of change of velocity ($a = \frac{dv}{dt}$).

3. Uniformly Accelerated Rectilinear Motion (UARM)

This is the most frequent topic. The prerequisite is that **Acceleration ($a$) is constant**.

#### A. The SUVAT Equations

Memorize these four equations and choose the right one based on known variables:

1. **Velocity-Time**: $$ v = v_0 + at $$

2. **Displacement-Time**: $$ x = v_0 t + \frac{1}{2}at^2 $$

3. **Velocity-Displacement** (No time $t$): $$ v^2 - v_0^2 = 2ax $$

4. **Average Velocity**: $$ \bar{v} = \frac{v_0 + v}{2} = \frac{x}{t} $$

#### B. Graphical Analysis

Graphs are shortcuts for solving problems, especially the **Velocity-Time (v-t) graph**:

* **Slope**: Represents Acceleration ($a$).

* **Area**: The area under the curve represents Displacement ($x$).

4. Typical Models & Traps

**Example: The Braking Trap**

A car travels at $20 \, \text{m/s}$ and brakes with an acceleration of $-4 \, \text{m/s}^2$. Find the displacement in the first $6 \, \text{s}$.

**Solution Strategy**:

1. **Check Stop Time**: Always calculate how long it takes to stop first.

$$ t_{stop} = \frac{0 - v_0}{a} = \frac{0 - 20}{-4} = 5 \, \text{s} $$

2. **Compare**: The question asks for $6 \, \text{s}$. Since $6 \, \text{s} > 5 \, \text{s}$, the car stops at $5 \, \text{s}$ and stays still for the last second.

3. **Calculate**: Calculate displacement for $5 \, \text{s}$ (not 6).

$$ x = \frac{v_0 + 0}{2} \cdot t_{stop} = \frac{20}{2} \times 5 = 50 \, \text{m} $$

*(Plugging in $t=6$ directly gives the incorrect answer of $48m$)*

5. Exam Tips

* **Sign Convention**: Always define a positive direction first (usually the direction of initial velocity). If speeding up, $a$ is positive; if slowing down, $a$ is negative.

* **Multi-stage Motion**: The final velocity of the first stage is the initial velocity of the second stage. This is the bridge connecting different parts of a problem.