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Forces and Motion - Calculating Speed and Velocity

Grade 6IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Speed is a scalar quantity that measures how fast an object moves regardless of direction. It is defined as the distance traveled per unit of time.

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Velocity is a vector quantity, which means it has both a magnitude (speed) and a specific direction. For example, 15 m/s15 \, m/s East is a velocity.

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Distance (dd) refers to the total length of the path traveled by an object, while Displacement (Δx⃗\Delta \vec{x}) is the straight-line distance between the starting and ending points including direction.

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The standard International System of Units (SI) for speed and velocity is meters per second (m/sm/s), though kilometers per hour (km/hkm/h) is also commonly used.

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Average speed is calculated by dividing the total distance by the total time taken: vavg=dtotalttotalv_{avg} = \frac{d_{total}}{t_{total}}.

📐Formulae

v=dtv = \frac{d}{t}

v⃗=Δx⃗t\vec{v} = \frac{\Delta \vec{x}}{t}

d=v×td = v \times t

t=dvt = \frac{d}{v}

💡Examples

Problem 1:

A toy car travels a distance of 1515 meters in 33 seconds. Calculate its speed.

Solution:

v=15 m3 s=5 m/sv = \frac{15 \, m}{3 \, s} = 5 \, m/s

Explanation:

To find the speed, we divide the total distance (15 m15 \, m) by the time taken (3 s3 \, s). The resulting speed is 55 meters per second.

Problem 2:

A bird flies 100100 meters North in 2020 seconds. What is the bird's velocity?

Solution:

v⃗=100 m North20 s=5 m/s North\vec{v} = \frac{100 \, m \text{ North}}{20 \, s} = 5 \, m/s \text{ North}

Explanation:

Velocity requires both speed and direction. We divide the displacement (100 m100 \, m North) by the time (20 s20 \, s) to get 5 m/s5 \, m/s in the direction of North.

Problem 3:

If a sprinter runs at a constant speed of 8 m/s8 \, m/s for 1212 seconds, how far do they travel?

Solution:

d=8 m/s×12 s=96 md = 8 \, m/s \times 12 \, s = 96 \, m

Explanation:

To find the distance, we rearrange the speed formula to multiply speed by time (d=v×td = v \times t). 8×128 \times 12 gives a total distance of 9696 meters.

Calculating Speed and Velocity - Revision Notes & Key Formulas | IB Grade 6 Science