4.2 Linear motion with constant acceleration

• Terms used in linear motion: distance, displacement, speed, velocity, acceleration
• Equations of linear motion (no derivations required)
• Examples of linear motion with constant acceleration in real life
• Freely falling bodies

• explain terms used in linear motion
• calculate variables of motion using the equations of linear motion
• carry out experiments on the effect of gravity on bodies under free fall
• appreciate the significance of linear motion and free fall in real life

“Why do we learn linear motion?”

“Do heavy objects really fall faster than light ones?”

“What are the dangers of free fall in day-to-day life?”

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1. Describing motion, and the four equations
   40 min · 2 practice tasks · quiz
   The words physics uses for movement, why two of them are not the same, and how to calculate any of them.
2. Free fall and the acceleration due to gravity
   40 min · 2 practice tasks · quiz
   Whether heavy things really fall faster, how to measure g, and why terminal velocity exists.
3. Distance and displacement on real journeys
   40 min · 1 practice tasks · quiz
   Distance is the path; displacement is the straight line from start to finish with a direction — a market walk and a running track make the difference physical.
4. Speed, units and average speed
   40 min · 1 practice tasks · quiz
   Average speed is total distance over total time; convert km/h to m/s by dividing by 3.6 before using the equations of motion.
5. Velocity and relative speed
   40 min · 1 practice tasks · quiz
   Velocity is speed in a stated direction; two vehicles meeting or overtaking need a relative speed, and a constant-speed turn is still a changing velocity.
6. Acceleration, second by second
   40 min · 1 practice tasks · quiz
   Acceleration is the change of velocity each second; 3 m/s² adds 3 m/s every second, and a negative value is slowing down, not a mistake.
7. Using v = u + at
   40 min · 1 practice tasks · quiz
   When displacement is not involved, the first equation finds v, u, a or t; list the five quantities, then substitute with signs.
8. Using s = ut + ½at²
   40 min · 1 practice tasks · quiz
   When final velocity is unknown, displacement from rest is ½at²; never forget to square the time.
9. Using v² = u² + 2as
   40 min · 1 practice tasks · quiz
   When time is unknown, the third equation links the two speeds to distance; braking distance goes as the square of speed.
10. Using s = ((u + v)/2) × t
    40 min · 1 practice tasks · quiz
    When acceleration is unknown, displacement is the average of the two speeds multiplied by time — the same idea as the area of a trapezium on a v–t graph.
11. Distance–time graphs
    40 min · 1 practice tasks · quiz
    The gradient of a distance–time graph is speed; a horizontal line is a stop; a curve means speeding up or slowing down.
12. Velocity–time graphs: gradient and area
    40 min · 1 practice tasks · quiz
    Gradient of a v–t graph is acceleration; area under the line is distance; split awkward shapes into triangles and rectangles.
13. Measuring acceleration on a ramp
    40 min · 1 practice tasks · quiz
    From rest down a ramp, a = 2s/t²; measure length and time, repeat, and treat reaction time as the main error.
14. Constant acceleration around us
    40 min · 1 practice tasks · quiz
    Runways, lifts, athletics starts, bodas leaving a bump, and water falling over a weir are the same four equations in Kenyan settings.
15. Upward throws and the symmetric fall
    40 min · 1 practice tasks · quiz
    Take upward as positive so a = −g; at the top v = 0 but acceleration is still g; time up equals time down, and the ball returns at the same speed.
16. Stopping distances, falls and staying alive
    40 min · 1 practice tasks · quiz
    Thinking plus braking, the u² law, and why a fall from twice the height carries twice the impact energy — road and site safety as applied linear motion.