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Grade 10 · Core Mathematics · Lesson 3 of 14

Determining Velocity and Acceleration in Different Situations

A Grade 10 Core Mathematics CBE lesson from the sub-strand Linear Motion. In it, learners determine velocity, distance, and time taken using directional linear motion formulas.

Strand Measurements and GeometrySub-strand Linear MotionLesson code 10CM-29-L340 minutes · 3 slides

KICD learning outcome (b)

Determine velocity and acceleration in different situations.

By the end of this lesson, learners should be able to

  1. Determine velocity, distance, and time taken using directional linear motion formulas.
  2. Calculate positive acceleration when an object speeds up over a given time interval.
  3. Calculate negative acceleration (deceleration) when an object slows down or comes to rest.

Key vocabulary

Displacement
distance moved by an object in a specified straight-line direction from a reference point
A vehicle driving 120 km directly North undergoes a total displacement of 120 km North.
Acceleration
rate at which the velocity of an object changes over time in a given direction
A car changing velocity by 10 m/s in 5 seconds has acceleration 2 m/s².
Deceleration
rate at which an object slows down, represented mathematically as negative acceleration
Brakes applied to slow a bus from 15 m/s to 5 m/s produce deceleration.

Lesson preview

Slide 1 · Calculating Velocity, Distance, and Time in Directional MotionOpening · 12 min
A boat moving East on a lake and a bus travelling North on a highway illustrate that velocity incorporates a specific direction.
Figure 1: A boat moving East on a lake and a bus travelling North on a highway illustrate that velocity incorporates a specific direction.

Velocity extends speed by incorporating direction into motion. To solve linear motion problems involving velocity, displacement, distance, and time, we apply uniform conversions between hours and seconds or kilometres and metres. Dividing displacement by time yields velocity in specific directions like East or North. Rearranging this relationship allows us to calculate total distance covered or time taken for trips across geographical regions accurately. See Figure 1 for examples of objects moving with velocities in specific directions.

  • Velocity specifies both magnitude and direction, whereas speed only measures how fast an object travels.
  • Calculate time by dividing total distance or displacement by average speed or velocity in consistent units.
  • Convert time to seconds when multiplying by velocity given in metres per second to obtain metres.
  • Expressing final velocity requires stating both the calculated numerical rate and the geographical direction travelled.
Worked example. Convert time for ferry to seconds: t=12×60 s=720 s. Calculate ferry distance: s=v×t=7 m/s×720 s=5040 m. Calculate bus velocity: v=DisplacementTime=210 km3.5 h=60 km/h due North. Answer: Distance covered by ferry is 5040 m; bus velocity is 60 km/h due North..

Check question: A cyclist rides at a constant velocity of 18 km/h due South. How many minutes will it take to cover a displacement of 15 km due South?

  1. 50
  2. 72
  3. 0.83
  4. 270
Show answer

50. Time in hours is calculated by dividing displacement by velocity: t=15 km18 km/h=56 h. Converting this to minutes gives 56×60=50 minutes.

Slide 2 · Determining Positive AccelerationModel · 14 min
A motorcycle travels along a straight path, accelerating from an initial velocity of 8 metres per second to 26 metres per second over 6 seconds.
Figure 2: A motorcycle travels along a straight path, accelerating from an initial velocity of 8 metres per second to 26 metres per second over 6 seconds.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • All 3 slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 13 lessons in this sub-strand
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All 14 lessons in Linear Motion

  1. 1Distance, Displacement, Speed, Velocity and AccelerationExplain the terms distance, displacement, speed, velocity and acceleration in real-life situations
  2. 2Determining Velocity and AccelerationDetermine velocity and acceleration in different situations
  3. 3Determining Velocity and Acceleration in Different SituationsDetermine velocity and acceleration in different situations
  4. 4Drawing Displacement-Time Graphs in Linear MotionDraw a displacement-time graph of different situations
  5. 5Interpreting Displacement-Time GraphsInterpret displacement-time graph in different situations
  6. 6Interpreting Displacement-Time Graphs in Different SituationsInterpret displacement-time graph in different situations
  7. 7Drawing Velocity-Time Graphs from Data TablesDraw a velocity-time graph from given tables in different situations
  8. 8Drawing Velocity-Time Graphs from Data Tables: Deceleration and ScenariosDraw a velocity-time graph from given tables in different situations
  9. 9Interpreting Velocity-Time Graphs in Linear MotionInterpret velocity-time graph in different situations
  10. 10Interpreting Velocity-Time Graphs in Practical SituationsInterpret velocity-time graph in different situations
  11. 11Relative Speed in Linear MotionDetermine relative speed of two moving bodies in different situations
  12. 12Relative Speed in Linear Motion: Advanced ApplicationsDetermine relative speed of two moving bodies in different situations
  13. 13Appreciating Linear Motion in Real-Life SituationsAppreciate use of linear motion in real-life situations
  14. 14Real-Life Applications of Linear MotionAppreciate use of linear motion in real-life situations