# **Exercise Questions** All questions in this exercise are listed below. Click on a question to view its solution. --- # **Key Concepts** This exercise focuses on the following concepts: - Displacement-time graphs and their interpretation - Velocity-time graphs and their interpretation - Distance, speed, and time relationships - Acceleration and deceleration in linear motion - Constant velocity and periods of rest - Calculating displacement from velocity-time graphs (area under curve) - Determining velocity from displacement-time graphs (gradient) --- # **Important Formulas** Below are the key formulas used in this exercise: **Distance, Speed, and Time:** $$v = \frac{d}{t} \quad \text{or} \quad d = v \times t \quad \text{or} \quad t = \frac{d}{v}$$ **Average Speed:** $$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$$ **Acceleration:** $$a = \frac{v - u}{t}$$ Where $u$ = initial velocity, $v$ = final velocity, $t$ = time interval **Graphical Relationships:** | Graph Type | Gradient Represents | Area Under Curve Represents | | :--- | :--- | :--- | | Displacement-Time | Velocity | — | | Velocity-Time | Acceleration | Displacement | --- # **Summary** This exercise covers linear motion analysis using both algebraic methods and graphical interpretation. Key skills include constructing and interpreting displacement-time and velocity-time graphs, calculating distance, speed, and acceleration for objects with constant velocity or uniform acceleration, and analyzing multi-stage journeys involving periods of motion, rest, and return trips. Emphasis is placed on understanding the relationships between graphical features (gradients and areas) and physical quantities: velocity equals the gradient of a displacement-time graph, while displacement equals the area under a velocity-time graph.