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Forces and Motion - Speed, Distance, and Time Calculations

Grade 7IB

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

🔑Concepts

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Speed is a scalar quantity that describes how fast an object is moving. It is defined as the distance traveled per unit of time: s=dts = \frac{d}{t}.

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Distance is the total length of the path traveled by an object, measured in meters (mm), kilometers (kmkm), or centimeters (cmcm).

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Time is the duration during which the motion occurs, measured in seconds (ss), minutes (minmin), or hours (hh).

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The standard SI unit for speed is meters per second (m/sm/s), although kilometers per hour (km/hkm/h) is frequently used for vehicles.

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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}}.

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On a Distance-Time graph, the gradient (slope) of the line represents the speed of the object. A horizontal line indicates the object is stationary (0 m/s0 \text{ m/s}).

📐Formulae

Speed(s)=Distance(d)Time(t)Speed (s) = \frac{Distance (d)}{Time (t)}

Distance(d)=Speed(s)×Time(t)Distance (d) = Speed (s) \times Time (t)

Time(t)=Distance(d)Speed(s)Time (t) = \frac{Distance (d)}{Speed (s)}

💡Examples

Problem 1:

A cyclist travels a distance of 45 km45 \text{ km} in 3 hours3 \text{ hours}. What is the average speed of the cyclist?

Solution:

s=45 km3 h=15 km/hs = \frac{45 \text{ km}}{3 \text{ h}} = 15 \text{ km/h}

Explanation:

To find the speed, we divide the total distance (45 km45 \text{ km}) by the total time (3 h3 \text{ h}). The resulting unit is km/h\text{km/h}.

Problem 2:

An athlete runs at a constant speed of 8 m/s8 \text{ m/s} for 25 seconds25 \text{ seconds}. How far does the athlete run?

Solution:

d=8 m/s×25 s=200 md = 8 \text{ m/s} \times 25 \text{ s} = 200 \text{ m}

Explanation:

To find the distance, we multiply the speed (8 m/s8 \text{ m/s}) by the time (25 s25 \text{ s}). The 'seconds' units cancel out, leaving the distance in meters (mm).

Problem 3:

A train is traveling at a steady speed of 120 km/h120 \text{ km/h}. How long will it take to travel a distance of 300 km300 \text{ km}?

Solution:

t=300 km120 km/h=2.5 hourst = \frac{300 \text{ km}}{120 \text{ km/h}} = 2.5 \text{ hours}

Explanation:

To find the time, we divide the distance (300 km300 \text{ km}) by the speed (120 km/h120 \text{ km/h}). The result is 2.52.5 hours, which can also be expressed as 2 hours and 30 minutes2 \text{ hours and } 30 \text{ minutes}.