DSE Physics Practice: Kinematics

DSE Physics Practice: Kinematics

18 MCQ practice problems on kinematics. Select an answer, submit, and review the explanation. Questions follow the DSE examination style and cover the full kinematics syllabus.

Scalars and Vectors

Practice Problem Tips

• Read the direction carefully: many questions have negative signs embedded in the setup. A ball thrown upward has u > 0 and a = -9.81 m/s². Always define your positive direction at the start of the problem.
• Draw a diagram: for multi-stage problems (e.g., a car accelerating then braking), sketch a v-t graph to visualise the motion before solving. This helps identify when velocity changes sign or when acceleration changes.
• Check units: DSE questions sometimes mix km/h with m/s. Convert first using 1 m/s = 3.6 km/h. A common trap is giving velocity in km/h but expecting displacement in metres.
• Identify the type of motion: is it constant velocity (a = 0), constant acceleration (use SUVAT), or changing acceleration (use graphs)? Choosing the wrong approach wastes time.
• Work backwards from what’s asked: if the question asks for time, identify which SUVAT equation contains time and the known variables. Don’t substitute into the first equation you see.

Approach Strategy

• Identify which SUVAT variables are known and which is unknown. List them explicitly: u = ?, v = ?, a = ?, s = ?, t = ?.
• If time is not involved, use v² = u² + 2as. This is the most common equation in DSE kinematics questions.
• For projectile problems, split into horizontal (constant velocity) and vertical (constant acceleration) components. The time component links both.
• For multi-stage problems (e.g., a ball thrown up and caught), set up separate equations for each stage and link them through the final state of one stage being the initial state of the next.
• When interpreting graphs, remember: gradient of s-t graph = velocity, gradient of v-t graph = acceleration, area under v-t graph = displacement.

Intuition

Think of each practice question as a mini-story about an object moving. First, understand the story: what is moving, what forces act on it, and what is being asked. Then translate the story into equations. The key skill in DSE kinematics is not memorising formulas but recognising which formula to apply. A good strategy is to write down all known quantities, identify the unknown, and then select the equation that links them. For graph-based questions, practise reading values from axes and calculating gradients and areas quickly.

Worked Examples

Example 1: SUVAT with Sign Convention

Problem: A ball is thrown vertically upward at 15 m/s from the top of a 20 m building. Find the time when it hits the ground. ($g = 9.81$ m/s²)

Solution: Step 1: Define sign convention: upward = positive, so $a = -g = -9.81$ m/s²

Step 2: When the ball hits the ground, displacement $s = -20$ m (below starting point)

Step 3: Use $s = ut + \frac{1}{2}at^2$: $-20 = 15t - 4.905t^2$

Step 4: Rearrange: $4.905t^2 - 15t - 20 = 0$

Step 5: Quadratic formula: $t = \frac{15 \pm \sqrt{225 + 4(4.905)(20)}}{9.81} = \frac{15 \pm \sqrt{616.4}}{9.81} = \frac{15 \pm 24.83}{9.81}$

Step 6: $t = \frac{39.83}{9.81} = 4.06$ s (reject negative root)

Key insight: Always define your sign convention before writing equations. The displacement is negative because the ground is below the starting point.

Example 2: Projectile Motion

Problem: A ball is thrown horizontally at 20 m/s from a cliff 45 m high. Find the horizontal distance when it hits the ground. ($g = 9.81$ m/s²)

Solution: Step 1: Vertical motion (u = 0, a = g, s = 45): $s = ut + \frac{1}{2}at^2 \Rightarrow 45 = 0 + 4.905t^2$

Step 2: Solve for $t$: $t^2 = \frac{45}{4.905} = 9.175 \Rightarrow t = 3.03$ s

Step 3: Horizontal motion (constant velocity): $d = vt = 20 \times 3.03 = 60.6$ m

Key insight: Horizontal and vertical motions are independent. The time of flight is determined entirely by the vertical motion.

Example 3: v-t Graph Interpretation

Problem: A car accelerates from rest at 2 m/s² for 5 s, then maintains constant velocity for 10 s, then decelerates to rest in 4 s. Find the total distance travelled.

Solution: Step 1: Draw the v-t graph (trapezium shape)

Step 2: Calculate velocities:

• After acceleration: $v = 0 + 2 \times 5 = 10$ m/s
• After constant velocity: $v = 10$ m/s
• After deceleration: $v = 0$ m/s

Step 3: Area under v-t graph = displacement:

• Triangle: $\frac{1}{2} \times 5 \times 10 = 25$ m
• Rectangle: $10 \times 10 = 100$ m
• Triangle: $\frac{1}{2} \times 4 \times 10 = 20$ m

Step 4: Total distance = $25 + 100 + 20 = 145$ m

Key insight: The area under a v-t graph gives displacement. For complex motion, break the graph into simple shapes (triangles, rectangles, trapeziums).

Common Mistakes

• Forgetting to square velocity: in v² = u² + 2as, students often write v = u + 2as or forget the square entirely. Always double-check that you are using the squared form.
• Mixing up initial and final velocity: u is initial (at t = 0), v is final (at time t). Swapping them gives wrong answers. Label your variables evidently before solving.
• Not converting units: if displacement is in metres, time in seconds, then velocity must be in m/s. Mixing km/h with m/s leads to incorrect magnitudes. A car at 72 km/h is moving at 20 m/s.
• Ignoring sign conventions: if upward is positive, then g = -9.81 m/s² and a downward initial velocity is negative. Sign errors propagate through calculations.
• Assuming horizontal motion affects vertical motion: in projectile problems, the horizontal and vertical components are independent. A ball thrown horizontally from a cliff has the same time of flight as one dropped from the same height.

Cross-References

• Mechanics: Kinematics is part of mechanics; dynamics (forces) builds on these concepts.
• Waves: Wave motion involves periodic kinematics; oscillatory motion connects to simple harmonic motion.
• Electricity: Circuit analysis uses similar mathematical techniques (rate of change, area under curves).
• Mathematics Compulsory: Quadratic equations and trigonometry are directly applied in kinematics problems.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.

Advanced Content

This section provides detailed coverage of advanced concepts, including full derivations, proofs, and extended examples.

Derivations and Proofs

Complete mathematical derivations and proofs are provided where appropriate. Each step is explained to ensure understanding of the underlying reasoning.

Extended Examples

Advanced examples demonstrate the application of concepts to complex problems. These examples go beyond standard exam questions to develop deeper understanding.

Research Connections

This material connects to current research and advanced applications in the field. Understanding these connections provides context for the study material.

Prerequisites

Ensure you have mastered the prerequisite material before attempting this advanced content.