(Average) Speed (symbol
) is the distance travelled (
) divided by the time taken (
) for the journey. Distance and time are scalars and therefore speed will also be a scalar. Speed is calculated as follows:
Instantaneous speed is the magnitude of instantaneous velocity. It has the same value, but no direction.
James walks 2 km away from home in 30 minutes. He then turns around and walks back home along the same path, also in 30 minutes. Calculate James' average speed and average velocity.
The question explicitly gives
the distance and time out (2 km in 30 minutes)
the distance and time back (2 km in 30 minutes)
The information is not in SI units and must therefore be converted.
To convert km to m, we know that:
Similarly, to convert 30 minutes to seconds,
James started at home and returned home, so his displacement is 0 m.
James walked a total distance of 4 000 m (2 000 m out and 2 000 m back).
James took 1 800 s to walk out and 1 800 s to walk back.
A man runs around a circular track of radius
. It takes him
to complete a revolution of the track. If he runs at constant speed, calculate:
his speed,
his instantaneous velocity at point A,
his instantaneous velocity at point B,
his average velocity between points A and B,
his average speed during a revolution.
his average velocity during a revolution.
To determine the man's speed we need to know the distance he travels and
how long it takes. We know it takes 120 s to complete one revolution ofthe track.(A revolution is to go around the track once.)
What distance is one revolution of the track? We know the
track is a circle and we know its radius, so we can determinethe distance around the circle. We start with
the equation for the circumference of a circle
Therefore, the distance the man covers in one revolution is
.
We know that speed is distance covered per unit time. So if we divide the distance covered by the time it took we will know how much distance was covered for every unit of time. No direction is used here because speed is a scalar.
Consider the point A in the diagram.
We know which way the man is running around the track and we know hisspeed. His velocity at point A will be his speed (the magnitude of the
velocity) plus his direction of motion (the direction of hisvelocity).
The instant that he arrives at A he is moving as indicated in thediagram.
His velocity will be
West.
Consider the point B in the diagram.
We know which way the man is running around the track and we know hisspeed. His velocity at point B will be his speed (the magnitude of the
velocity) plus his direction of motion (the direction of hisvelocity). The instant that he arrives at B he is moving as indicated in
the diagram.His velocity will be
South.
To determine the average velocity between A and B, we need the change in
displacement between A and B and the change in time between A and B. Thedisplacement from A and B can be calculated by using the Theorem of Pythagoras:
The time for a full revolution is 120 s, therefore the time for a
of a revolution is 30 s.
Velocity is a vector and needs a direction.
Triangle AOB is isosceles and therefore angle BAO = 45
.
The direction is between west and south and is therefore southwest.
The final answer is:
, southwest.
Because he runs at a constant rate, we know that his speed anywhere around
the track will be the same. His average speed is
.
Remember - displacement can be zero even when distance
travelled is not!
To calculate average velocity we need his total displacement and his total
time. His displacement is zero because he ends up where he started. Histime is
.
Using these we can calculate his average velocity:
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Samuel
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