9.2 Speed and velocity

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Speed, average velocity and instantaneous velocity

Velocity

Velocity is the rate of change of displacement.

Instantaneous velocity

Instantaneous velocity is the velocity of a body at a specific instant in time.

Average velocity

Average velocity is the total displacement of a body over a time interval.

Velocity is the rate of change of position. It tells us how much an object's position changes in time. This is the same as the displacement divided by the time taken. Since displacement is a vector and time taken is a scalar, velocity is also a vector. We use the symbol $v$ for velocity. If we have a displacement of $Δ x$ and a time taken of $Δ t$ , $v$ is then defined as:

\begin{matrix} velocity (in m \cdot s^{- 1}) & = & \frac{change in displacement (in m)}{change in time (in s)} \\ v & = & \frac{Δ x}{Δ t} \end{matrix}

Velocity can be positive or negative. Positive values of velocity mean that the object is moving away from the reference point or origin and negative values mean that the object is moving towards the reference point or origin.

An instant in time is different from the time taken or the time interval. It is therefore useful to use the symbol

t

for an instant in time (for example during the 4 ^th second) and the symbol

Δ t

for the time taken (for example during the first 5 seconds of the motion).

Average velocity (symbol $v$ ) is the displacement for the whole motion divided by the time taken for the whole motion. Instantaneous velocity is the velocity at a specific instant in time.

(Average) Speed (symbol $s$ ) is the distance travelled ( $d$ ) divided by the time taken ( $Δ t$ ) for the journey. Distance and time are scalars and therefore speed will also be a scalar. Speed is calculated as follows:

speed (in m \cdot s^{- 1}) = \frac{distance (in m)}{time (in s)}

s = \frac{d}{Δ t}

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.

Identify what information is given and what is asked for
The question explicitly gives
- the distance and time out (2 km in 30 minutes)
- the distance and time back (2 km in 30 minutes)
Check that all units are SI units.
The information is not in SI units and must therefore be converted.

To convert km to m, we know that:

$\begin{matrix} 1 km & = & 1 000 m \\ ∴ 2 km & = & 2 000 m (multiply both sides by 2, because we want to convert 2 km to m .) \end{matrix}$

Similarly, to convert 30 minutes to seconds,

$\begin{matrix} 1 \min & = & 60 s \\ ∴ 30 \min & = & 1 800 s (multiply both sides by 30) \end{matrix}$
Determine James' displacement and distance.
James started at home and returned home, so his displacement is 0 m.

$Δ x = 0 m$

James walked a total distance of 4 000 m (2 000 m out and 2 000 m back).

$d = 4 000 m$
Determine his total time.
James took 1 800 s to walk out and 1 800 s to walk back.

$Δ t = 3 600 s$
Determine his average speed
$\begin{matrix} s & = & \frac{d}{Δ t} \\ = & \frac{4 000 m}{3 600 s} \\ = & 1, 11 m \cdot s^{- 1} \end{matrix}$
Determine his average velocity
$\begin{matrix} v & = & \frac{Δ x}{Δ t} \\ = & \frac{0 m}{3 600 s} \\ = & 0 m \cdot s^{- 1} \end{matrix}$

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A man runs around a circular track of radius $100 m$ . It takes him $120 s$ 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.

Decide how to approach the problem
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.)
Determine the distance travelled
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

$\begin{matrix} C & = & 2 π r \\ = & 2 π (100 m) \\ = & 628, 32 m \end{matrix}$

Therefore, the distance the man covers in one revolution is $628,32 m$ .
Determine the speed
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.
$\begin{matrix} s & = & \frac{d}{Δ t} \\ = & \frac{628, 32 m}{120 s} \\ = & 5, 24 m \cdot s^{- 1} \end{matrix}$
Determine the instantaneous velocity at A
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 $5,24 m \cdot s^{- 1}$ West.
Determine the instantaneous velocity at B
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 $5,24 m \cdot s^{- 1}$ South.
Determine the average velocity between A and B
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:

$\begin{matrix} {(Δ x)}^{2} & = & {(100 m)}^{2} + {(100 m)}^{2} \\ = & 20000 m \\ Δ x & = & 141, 42135 . . . m \end{matrix}$
The time for a full revolution is 120 s, therefore the time for a $\frac{1}{4}$ of a revolution is 30 s.
$\begin{matrix} v_{A B} & = & \frac{Δ x}{Δ t} \\ = & \frac{141, 42 . . . m}{30 s} \\ = & 4.71 m \cdot s^{- 1} \end{matrix}$

Velocity is a vector and needs a direction.

Triangle AOB is isosceles and therefore angle BAO = 45 $^{\circ}$ .

The direction is between west and south and is therefore southwest.

The final answer is: $v = 4.71 m \cdot s^{- 1}$ , southwest.
Determine his average speed during a revolution
Because he runs at a constant rate, we know that his speed anywhere around the track will be the same. His average speed is $5,24 m \cdot s^{- 1}$ .
Determine his average velocity over a complete revolution
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 $120 s$ . Using these we can calculate his average velocity:

$\begin{matrix} v & = & \frac{Δ x}{Δ t} \\ = & \frac{0 m}{120 s} \\ = & 0 m \cdot s^{- 1} \end{matrix}$

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Questions & Answers

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is the branch of biology that deals with the study of microorganisms.

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studies of microbes

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Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments

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they make spores

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the significance of food webs for disease transmission

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food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.

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Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).

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This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products

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Examples of thermophilic organisms

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Give Examples of thermophilic organisms

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advantages of normal Flora to the host

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Prevent foreign microbes to the host

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they provide healthier benefits to their hosts

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They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!

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cell is the smallest unit of life

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Innocent

cell is the structural and functional unit of life

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is the fundamental units of Life

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There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️

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Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract

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skin

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part of a tissue or an organ being wounded or bruised.

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Binomial nomenclature

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Source: OpenStax, Siyavula textbooks: grade 10 physical science. OpenStax CNX. Aug 29, 2011 Download for free at http://cnx.org/content/col11245/1.3

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