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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

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}.

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

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

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.

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

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}.