Velocity | Speed |
---|---|

-Vector Rate of change of displacement in respect to time |
-Scalar Rate of change of distance in respect to time |

Acceleration |
---|

-Vector Rate of change of velocity in respect to time |

**Acceleration is a vector and thus has a direction. If we assume the upwards direction to be positive, the acceleration due to gravity would have a negative value.

*Slope is velocity

*Slope is acceleration **Area under the curve is displacement

*Area under the curve is change in velocity

*acceleration must be constant!

\begin{gather*}
v=\ u\ +\ at\ \\
\\
\ s\ =\ \frac{( u+v)}{2} t\ \\
\\
\ s\ =\ ut\ +\ \frac{1}{2} at^{2} \ \\
\\
\ s\ =\ vt\ –\ \frac{1}{2} at^{2} \ \\
\\
v^{2} \ =\ u^{2} \ +\ 2as\ \\
\\
\ v=final\ velocity,\ u=initial\ velocity,\ t=time\ taken,\ s=displacement,\ a=acceleration
\end{gather*}

An object follows a curved path due to the influence of gravity.

The horizontal component is constant

The vertical component accelerates downward at 9.81 ms^{-2}

The projective reaches maximum height when vertical velocity is 0

The trajectory is symmetric

The maximum height is lower

The trajectory is not symmetric

The range of projectile is shorter

When the force of air resistance is equal to the force of gravity on a falling object

The specific velocity at which one stops accelerating is known as terminal velocity

\begin{gather}
v=\sqrt{\frac{2mg}{\rho AC_{d}}}\\
m=mass,\ g=acceleration\ due\ to\ gravity,\ \rho =density\ of\ medium,\ A=area\ of\ object, \notag\\
C_{d} \ =drag\ coefficient\ of\ object \notag\\
\notag\\
\notag
\end{gather}

Table of common drag coefficients
ForcesUnit of force is Newtons are represented as arrows acting on a point mass.

The lenght and direction depends on the magnitude and direction of the force.

To determine resultant force:

**1.**Resolve the forces into vertical and horizontal components

**2.**Combine the sum of horizontal and vertical components

**3.**Find the angle by using tangent

The net force on the body is zero, so the body is at rest or travels at constant velocity.

**Examples:** elevator moving upwards at constant velocity, a falling man reaches terminal velocity.

*Published in Philosophiae Naturalis Principia Mathematica (1687)*

**1.**If a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. This postulate is known as the law of inertia.

**2.**F=ma

**3.**When two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction.

FrictionDenoted by µ is a force opposing motion, where to solid surfaces move against each other.

There are two types of friction for solids: static (stops object from beggining motion) and kinetic (slows down objects motion).

Static friction (µs) is larger than kinetic friction(µk).

\begin{gather*}
F=µ N\\
F\ =\ frictional\ force,µ \ =\ frictional\ coefficient,\ N\ =\ normal\ force\
\end{gather*}

\begin{gather*}
E_{k} =\frac{1}{2} mv^{2}\\
m=\ mass,\ v=velocity\\
\end{gather*}

\begin{gather*}
E_{p} =mgh\\
m=\ mass,\ g=acceleration\ due\ to\ gravity,\ h=height\\
\end{gather*}

\begin{gather*}
E_{p} =\frac{1}{2} kx^{2}\\
k=spring\ constant,\ x=extension\ of\ spring\\
\end{gather*}

\begin{gather*}
W=F*s*cos\theta \\
F=force,\ s=displacement,\ \theta =angle\ between\ force\ and\ direction\ of\ motion
\end{gather*}

In a force-displacement graph, work is the area under the curve

\begin{gather*}
P=\frac{W}{t}\\
W=work\ done,\ t=time\ taken
\end{gather*}

For a constant force acting on object with constant velocity:

\begin{gather*}
P=vF\\
F=force,\ v=velocity
\end{gather*}

Energy cannot be created or destroyed, only converted into different form. For example when kicking a football that is sitting on the ground, energy is transferred from the kicker's body to the ball, setting it in motion.

Demonstration of the conservation of energyTotal energy remains constant:

\begin{gather*}
\Delta KE+\Delta PE=0
\end{gather*}

\begin{equation}
Efficiency=\frac{useful\ energy\ output}{energy\ input} *100\%
\end{equation}

\begin{equation}
Efficiency=\frac{useful\ power\ output}{power\ input} *100\%
\end{equation}

\begin{gather*}
Linear\ momentum\ is\ given\ by:\\
\\
p\ =\ mv\\
\\
v\ =\ velocity,\ m=mass,\ p=momentum
\end{gather*}

It is a vector with the same direction as the velocityThe change of momentum is called impulse

\begin{gather*}
F\Delta t=m\Delta v\\
F\Delta t\ is\ the\ impulse,\ m=mass,\ v=velocity
\end{gather*}

The area under the force-time graph is impulse

In a closed system, the sum of initial momentum is equal to the sum of final momentum

\begin{gather}
m_{1} u_{1} +m_{2} u_{2} =m_{1} v_{1} +m_{2} v_{2}\\
m=mass,\ u=initial\ velocity,\ v=final\ velocity \notag
\end{gather}

Type | Total Momentum | Total Kinetic energy |
---|---|---|

Elastic | Conserved | Conserved |

Inelastic | Conserved | Not conserved |

Explosion | Conserved | Not conserved |

Number of correct answers: