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Where are we now and where might we be going - Speed- Distance- Time Relationship

Grade 7IB

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

🔑Concepts

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Distance (dd) is a scalar quantity that refers to how much ground an object has covered during its motion, measured in meters (mm) or kilometers (kmkm).

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Time (tt) is the duration over which movement occurs, measured in seconds (ss), minutes (minmin), or hours (hh).

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Speed (ss) is the rate at which an object covers distance. It is a scalar quantity, meaning it has magnitude but no specific direction.

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The Speed-Distance-Time triangle is a tool to remember the relationships: dd is at the top, and ss and tt are at the bottom.

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Average Speed is used when the speed of an object changes during a journey. It is calculated by dividing the total distance by the total time taken: Average Speed=Total DistanceTotal TimeAverage\ Speed = \frac{Total\ Distance}{Total\ Time}

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On a Distance-Time Graph, the gradient (slope) represents the speed of the object. A steeper line indicates a higher speed, while a horizontal line indicates the object is at rest (speed=0speed = 0).

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To convert from kilometers per hour (km/hkm/h) to meters per second (m/sm/s), multiply the value by 10003600\frac{1000}{3600} or divide by 3.63.6.

📐Formulae

s=dts = \frac{d}{t}

d=s×td = s \times t

t=dst = \frac{d}{s}

vavg=dtotalttotalv_{avg} = \frac{d_{total}}{t_{total}}

💡Examples

Problem 1:

A cyclist travels 4545 km in 33 hours. Calculate the average speed of the cyclist.

Solution:

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

Explanation:

To find the speed, we use the formula s=dts = \frac{d}{t}. Dividing the distance (4545 km) by the time (33 hours) gives us the speed of 1515 km/h.

Problem 2:

A train travels at a constant speed of 120120 km/h. How far will it travel in 1515 minutes?

Solution:

First, convert minutes to hours: t=1560=0.25 hourst = \frac{15}{60} = 0.25\text{ hours} Now, calculate distance: d=s×td = s \times t d=120 km/h×0.25 hd = 120\text{ km/h} \times 0.25\text{ h} d=30 kmd = 30\text{ km}

Explanation:

Since the speed is in km/h, the time must be converted to hours (1515 minutes is 0.250.25 hours). Multiplying speed by time gives the total distance.

Problem 3:

Convert a speed of 2020 m/s into km/h.

Solution:

20 m/s=20×3600 s1000 m20\text{ m/s} = 20 \times \frac{3600\text{ s}}{1000\text{ m}} 20 m/s=20×3.620\text{ m/s} = 20 \times 3.6 20 m/s=72 km/h20\text{ m/s} = 72\text{ km/h}

Explanation:

To convert meters per second to kilometers per hour, we multiply by 36003600 (seconds in an hour) and divide by 10001000 (meters in a kilometer), which is equivalent to multiplying by 3.63.6.