Mada za sehemu hiiSpeedMada 2
- The concept of speed
- Computation of speed
When two cars start a journey at the same time and cover the same distance, they can reach their final destinations at different times. If the cars do not stop until they reach their final destinations, the one with higher speed will arrive first. Likewise, in athletics, a winner runs at a high speed to cover the required distance in a short time. The distance covered per time taken when travelling, running, walking or swimming is called speed. The speed of moving bodies differs from one another. For example, an aeroplane moves at a higher speed than a car. Also, the speeds of some cars are higher than those of some motorbikes, and a motorbike moves at a higher speed than a bicycle. Aeroplanes, cars and motorbikes are some of the means of transport which use speedometers for measuring their speed.
An international standard football ground is approximated to have a perimeter of 0.328 kilometres. This means that a cheetah can run around the football ground 345 times per hour. That is, 113 kilometres/0.328 kilometres per hour = 345 times per hour. An eagle has the ability of flying at a speed of up to 320 kilometres per hour. This means that the eagle can fly around a football ground 975 times per hour. That is, 320 kilometres/0.328 kilometres per hour = 975 times per hour.
An athlete can run up to a distance of 37 kilometres per hour. This means that an athlete can run around the football ground 113 times per hour. That is, 37 kilometres/0.328 kilometres per hour = 113 times per hour.
Speed is the measure of distance moved in a given time. The time can be an hour, a minute or second. Therefore, the formula for speed is obtained by dividing the distance covered by the time taken. Thus,
From the speed formula, distance and time can be described as follows:
Distance is the length between two objects or points. The Standard International (SI) unit of distance is metre abbreviated as 'm'. Other units of distance include millimetre (mm), centimetre (cm), decimetre (dm), decametre (dam), hectometre (hm) and kilometre (km). The devices used for measuring distance can be tape measures and rulers.
Time refers to hours, minutes or seconds spent in moving from one point to another. The SI unit of time is second abbreviated as 's'. Other units used in measuring time include hours and minutes. A tool used for measuring time is called clock or watch. The stopwatch is used to measure the starting time and ending time of a certain event. The stopwatch can have a circular shape with minute and second arrows. Also, it can be a digital stopwatch which shows hours, minutes and seconds.
The unit of speed is obtained by dividing the unit of distance by the unit of time. For example, metre/second or kilometre/hour. However, the SI unit of speed is metre/second abbreviated as m/s.
If the values of two quantities among the distance, time and speed are known, the value of the other quantity can be obtained. The following table shows metric units and their symbols for distance, time and speed used in calculations.
| Distance | Time | Speed | Abbreviation |
|---|---|---|---|
| Kilometre (km) | Hour (hr) | Kilometre per hour | km/hr |
| Metre (m) | Hour (hr) | Metre per hour | m/hr |
| Metre (m) | Second (s) | Metre per second | m/s |
| Centimetre (cm) | Second (s) | Centimetre per second | cm/s |
Jane and Juma live in the same household and they both study at Juhudi Primary School. Juma spends 40 minutes to walk from home to school. Jane spends 30 minutes to walk from home to school using the same route. Who walks at a higher speed between the two?
Solution
Jane and Juma walk the same distance. Since the distance is the same, the person who spends a shorter time will have a higher speed. Jane spends 30 minutes and Juma spends 40 minutes. Thus, Jane spends a shorter time. Therefore, Jane walks at a higher speed than Juma.
The following graph shows the distance covered from point A to D against the time taken. Study the graph carefully, and then answer the questions that follow.
(a) What is the time taken to move from point A to B?
(b) What is the distance from point A to B?
(c) What is the time taken to move from point B to C?
(d) What is the distance from point B to C? Explain the meaning of the distance obtained.
(e) What is the time taken to move from point C to D?
(f) What is the distance from point C to D?
(g) Which part has a higher slope between moving from point A to B and C to D?
Solution
(a) The horizontal axis represents the time taken. Thus, the time taken from point A to B = The horizontal coordinate of point B minus horizontal coordinate of point A. That is,
Time taken from A to B = 4 seconds − 0 second = 4 seconds.
Therefore, the time taken to move from point A to B is 4 seconds.
(b) The distance from point A to B = The vertical coordinate of point B minus the vertical coordinate of point A. That is,
Distance from A to B = 2 metres − 0 metres = 2 metres.
Therefore, the distance from point A to B is 2 metres.
(c) The time taken from B to C = 8 seconds − 4 seconds = 4 seconds.
Therefore, the time taken from point B to C is 4 seconds.
(d) The distance from B to C = 2 metres − 2 metres = 0 metres.
Therefore, the distance from point B to C is 0 metres. This means that there is no movement between the points.
(e) The time taken from C to D = 10 seconds − 8 seconds = 2 seconds.
Therefore, the time taken from point C to D is 2 seconds.
(f) The distance from C to D = 6 metres − 2 metres = 4 metres.
Therefore, the distance from point C to D is 4 metres.
(g) The slope between the points A and B
= Vertical increase from point A to B / Horizontal increase from point A to B
= (2m − 0m) / (4s − 0s) = 2m/4s = 0.5 m/s.
The slope between the points C and D is 0.5 m/s.
The slope between the points C and D
= Vertical increase from point C to D / Horizontal increase from point C to D
= (6m − 2m) / (10s − 8s) = 4m/2s = 2 m/s.
The slope between the points C and D is 2 m/s.
Therefore, the slope from C to D is higher than that from A to B.
Carefully study the following graph showing the speed of three athletes, and then answer the questions that follow.
(a) Which athlete had the highest speed? Give reasons.
(b) Which athlete used longer time than others?
(c) What distance did each athlete run?
Solution
(a) The graph shows that all the athletes ran a distance of 6 kilometres. Musa spent 3 hours, Mary used 6 hours and Ali used 10 hours. Therefore, Musa ran at the highest speed because he covered the distance in a shorter time than others.
(b) Ali spent more time to run the same distance of 6 kilometres.
(c) Each athlete ran a distance of 6 kilometres.
Swali
Which formula is used to calculate speed?
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