Chapter summary
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21.7 Equations of motion

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Chapter summary

A reference point is a point from where you take your measurements.

A frame of reference is a reference point with a set of directions.

Your position is where you are located with respect to your reference point.

The displacement of an object is how far it is from the reference point. It is the shortest distance between the object and the reference point. It has magnitude and direction because it is a vector.

The distance of an object is the length of the path travelled from the starting point to the end point. It has magnitude only because it is a scalar.

Speed (\(v\)) is the distance covered (\(D\)) divided by the time taken (\(\Delta t\))
\[v=\frac{D}{\Delta t}\] 
Average velocity (\({\vec{v}}_{av}\)) is the displacement (\(\Delta \vec{x}\)) divided by the time taken (\(\Delta t\)):
\[{\vec{v}}_{av}=\frac{\Delta \vec{x}}{\Delta t}\] 
Instantaneous speed is the speed at a specific instant in time.

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

Acceleration (\(\vec{a}\)) is the change in velocity (\(\Delta \vec{v}\)) over a time interval (\(\Delta t\)):
\[\vec{a}=\frac{\Delta \vec{v}}{\Delta t}\] 
The gradient of a position  time graph (\(x\) vs. \(t\)) gives the velocity.

The gradient of a velocity  time graph (\(v\) vs. \(t\)) gives the acceleration.

The area under a velocity  time graph (\(v\) vs. \(t\)) gives the displacement.

The area under an acceleration  time graph (\(a\) vs. \(t\)) gives the velocity.

The graphs of motion are summarised in Figure 21.7.

The equations of motion are used where constant acceleration takes place:
\begin{align*} {v}_{f} & = {v}_{i} + at \\ \Delta \vec{x} & = \frac{\left({v}_{i} + {v}_{f}\right)}{2}t \\ \Delta \vec{x} & = {v}_{i}t + \frac{1}{2}a{t}^{2} \\ {\vec{v}}_{f}^{2} & = {\vec{v}}_{i}^{2} + 2a\Delta \vec{x} \end{align*}
Physical Quantities 

Quantity 
Vector 
Unit name 
Unit symbol 
Position (\(x\)) 
 
metre 
m 
Distance (\(D\)) 
 
metre 
m 
Displacement (\(\Delta \vec{x}\)) 
✓ 
metre 
m 
Speed (\({v}_{av}\)) 
 
metre per second 
\(\text{m·s$^{1}$}\) 
Average velocity (\({\vec{v}}_{av}\)) 
✓ 
metre per second 
\(\text{m·s$^{1}$}\) 
Instantaneous velocity (\(\vec{v}\)) 
✓ 
metre per second 
\(\text{m·s$^{1}$}\) 
Instantaneous speed (\(v\)) 
 
metre per second 
\(\text{m·s$^{1}$}\) 
Instantaneous acceleration (\(\vec{a}\)) 
✓ 
metre per second per second 
\(\text{m·s$^{2}$}\) 
Average acceleration (\({\vec{a}}_{av}\)) 
✓ 
metre per second per second 
\(\text{m·s$^{2}$}\) 
Magnitude of acceleration (\(a\)) 
 
metre per second per second 
\(\text{m·s$^{2}$}\) 
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21.7 Equations of motion

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