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Linear motion — KCSE Physics

KCSE Physics · 117 practice questions · 8 syllabus objectives · 8 revision lessons

39 easy38 medium40 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Define distance, displacement, speed, velocity and acceleration

Describe experiments to determine velocity and acceleration

Determine acceleration due to gravity using free fall and simple pendulum

Plot and explain displacement-time and velocity-time graphs

Apply the equations of uniformly accelerated motion v=u+at, s=ut+½at², v²=u²+2as

Solve numerical problems on uniformly accelerated motion including vertical projection and horizontal projection

Determine velocity and acceleration using ticker-timer experiments

Use calculus (differentiation and integration) to determine velocity, acceleration and displacement from given functions of time

Revision Notes

Concise lesson notes for Linear motion, written to the KCSE Physics marking standard. Read the first lesson free below.

Key Concepts in Linear Motion

In physics, understanding linear motion involves defining several key terms:

  • Distance: This is the total path length traveled by an object, regardless of direction. It is a scalar quantity and is measured in meters (m).
  • Displacement: This is the shortest straight-line distance from the initial to the final position of an object. It is a vector quantity, having both magnitude and direction.
  • Speed: This is the rate at which an object covers distance. It is a scalar quantity and is calculated as speed = distance/time (m/s).
  • Velocity: This is the rate of change of displacement. It is a vector quantity and is calculated as velocity = displacement/time (m/s).
  • Acceleration: This is the rate of change of velocity over time. It is a vector quantity and is calculated as acceleration = (final velocity - initial velocity)/time (m/s²).

Understanding these definitions is crucial for solving problems related to motion in physics. Always remember to distinguish between scalar and vector quantities, as this affects calculations and interpretations.

Key points to remember

  • Distance is a scalar quantity; it measures total path length.
  • Displacement is a vector; it measures shortest path with direction.
  • Speed is distance traveled per unit time; it's scalar.
  • Velocity is displacement per unit time; it's vector.
  • Acceleration is change in velocity over time; it's vector.

Worked example

Define speed and provide its formula.

  • Speed is the rate at which an object covers distance.
  • Formula: Speed = Distance / Time.

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Lesson 2: Experiments to Measure Velocity and Acceleration

Objective: Describe experiments to determine velocity and acceleration

To determine velocity and acceleration, we can perform simple experiments using a toy car and a stopwatch. Velocity is the rate of change of displacement, while acceleration is the rate of change of velocity.

Experiment to Determine Velocity: 1. Set up a ramp and release a toy car from a known height. 2. Measure the distance the car travels using a measuring tape. 3. Use a stopwatch to time how long it takes the car to reach the end of the measured distance. 4. Calculate velocity using the formula:

[ \text{Velocity} = \frac{\text{Distance}}{\text{Time}} ]

Experiment to Determine Acceleration: 1. Use the same ramp setup and car. 2. Release the car from the same height multiple times to gather time data. 3. Record the time taken for each run. 4. Calculate acceleration using the formula:

[ \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}} ]

Repeat the experiment several times for accuracy and average your results.

  • Velocity is distance traveled over time.
  • Acceleration is the change in velocity over time.
  • Use a stopwatch to measure time accurately.
  • Repeat experiments for reliable results.
  • Record all measurements clearly for analysis.

A toy car travels 5 meters in 2 seconds. Calculate its velocity.

  • Velocity = Distance / Time = 5 m / 2 s = 2.5 m/s.
Lesson 3: Determining Acceleration Due to Gravity

Objective: Determine acceleration due to gravity using free fall and simple pendulum

To determine the acceleration due to gravity (g), we can use two methods: free fall and the simple pendulum.

  1. Free Fall Method:

    • Drop an object from a known height (h).

    • Measure the time (t) it takes to hit the ground.

    • Use the formula:

      [ g = \frac{2h}{t^2} ]

    • This formula derives from the equation of motion: ( s = ut + \frac{1}{2}gt^2 ) (where initial velocity u = 0).

  2. Simple Pendulum Method:

    • Suspend a pendulum and measure its length (L).

    • Measure the time period (T) for multiple oscillations and divide by the number of oscillations to find the average period.

    • Use the formula:

      [ g = \frac{4\pi^2L}{T^2} ]

    • This formula comes from the relationship between the period of a pendulum and gravitational acceleration.

Both methods should yield a value of approximately 9.81 m/s² for g, which is the standard acceleration due to gravity on Earth.

  • Free fall measures time and height to calculate g.
  • Use g = 2h/t² for free fall calculations.
  • Pendulum length and period determine g using g = 4π²L/T².
  • Both methods should approximate 9.81 m/s².

A ball is dropped from a height of 20 m. It takes 2 seconds to reach the ground. Calculate g.

  • Using g = 2h/t²:
    g = 2(20 m)/(2 s)² = 20 m/s².
    Therefore, g = 5 m/s².
Lesson 4: Understanding Displacement-Time and Velocity-Time Graphs

Objective: Plot and explain displacement-time and velocity-time graphs

Displacement-time and velocity-time graphs are essential tools in understanding linear motion.

Displacement-Time Graphs:

  • The slope represents velocity.
  • A straight line indicates uniform motion.
  • A horizontal line indicates rest.
  • A steep slope indicates high velocity, while a gentle slope indicates low velocity.

Velocity-Time Graphs:

  • The slope represents acceleration.
  • A horizontal line indicates constant velocity.
  • An upward slope indicates positive acceleration, while a downward slope indicates negative acceleration (deceleration).

Key Features:

  • The area under the velocity-time graph represents displacement.
  • The steeper the slope in both graphs, the greater the change in motion.

To interpret these graphs accurately, identify the axes: displacement (y-axis) versus time (x-axis) for displacement-time graphs, and velocity (y-axis) versus time (x-axis) for velocity-time graphs. Understanding these concepts helps in analyzing motion effectively.

  • Displacement-time graphs show how position changes over time.
  • Velocity-time graphs indicate how speed changes over time.
  • The slope of a displacement-time graph equals velocity.
  • The slope of a velocity-time graph equals acceleration.
  • Area under a velocity-time graph equals total displacement.

Plot the displacement-time graph for an object moving at constant speed.

  • The graph will be a straight line with a positive slope, indicating uniform motion.

Sample Questions

Read 3 questions and answers free. Sign up to access all 117 questions with full KNEC-style marking schemes and a personalised study plan.

1
easySHORT ANSWER4 marks

A ball is dropped from a height of 20 m. (Take g = 10 m/s²) (a) Define the term 'free fall'. (1 mark) (b) Calculate the time taken for the ball to reach the ground. (3 marks)

Answer & marking scheme

Part (a) — 1 mark
Free fall is the motion of a body under the influence of gravity only, with no air resistance. (1 mk)
Part (b) — 3 marks
Using the formula s = ut + ½gt², where u = 0, s = 20 m, and g = 10 m/s² (1 mk)
Substituting values gives 20 = 0 × t + ½ × 10 × t² (1 mk)
Solving the equation gives t = 2 s (with correct units) (1 mk)
2
easySHORT ANSWER4 marks

A vehicle accelerates uniformly from a speed of 15 m/s to a speed of 25 m/s over a time period of 5 seconds. (a) Calculate the acceleration of the vehicle. (2 marks) (b) Determine the distance covered during this time. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
a = (v - u) / t = (25 - 15) / 5 (1 mk)
Correct value with units m/s² (2 m/s²) (1 mk)
Part (b) — 2 marks
s = ut + ½at² = (15 * 5) + ½ * 2 * (5²) (1 mk)
Correct value with units m (75 m) (1 mk)
3
easySHORT ANSWER2 marks

State what the slope of a velocity-time graph represents. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
The slope represents acceleration (1 mk)
A positive slope indicates increasing velocity (1 mk)
4

Define the following terms related to linear motion: (a) distance (1 mark) (b) displacement (1 mark) (c) speed (1 mark) (d) velocity (1 mark) (e) acceleration (1 mark)

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Frequently asked questions

What does the KCSE Physics topic "Linear motion" cover?

Distance, displacement, speed, velocity, acceleration, motion graphs, equations of motion, free fall, projectiles

How many practice questions are available for Linear motion?

HighMarks has 117 Linear motion practice questions for KCSE Physics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Physics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Linear motion for the KCSE exam?

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