2.1 Motion

Displacement and Distance

Velocity and Speed

Velocity Speed
Rate of change of displacement in respect to time
Rate of change of distance in respect to time
Velocity is a measure dependent on the motion of the observer. The relative velocity of A to B is equal to the vector subtraction of the velocity of B from the velocity of A.


Rate of change of velocity in respect to time
*Acceleration due to gravity = 9.8 m/s2. Does not depend on mass of the object.
**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.

Motion Graphs

Displacement-time graph

*Slope is velocity

Velocity-time graph

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

Acceleration-time graph

*Area under the curve is change in velocity

Understanding with calculus

Motion graphs help tool

Suvat equations

*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*}

Projectile motion

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

If no air resistance:

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

If air resistance is present:

The maximum height is lower

The trajectory is not symmetric

The range of projectile is shorter

Terminal velocity

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

2.2 Forces

Free body diagrams

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

Transitional equilibrium

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.

Newton's laws of motion

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.


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*}

Table of common frictional coefficients

2.3 Work, energy, and power

Kinetic energy

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

Gravitational potential energy

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

Elastic potential energy

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

Work done

\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*}

Conservation of energy

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 energy

Total 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}

2.4 Momentum

Linear momentum

\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 velocity
The change of momentum is called impulse

Impulse formula

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

Impulse and force-time graphs

The area under the force-time graph is impulse

Conservation of linear momentum

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

Topic 2 Problems

1. Using the graph, determine the acceleration during the first 8 seconds.

A. 2ms-2

B. 4ms-2

C. 8ms-2

D. 1ms-2

2. A car of mass 1000 kg accelerates on a straight fat horizontal road with an acceleration a = 0.30 m s–2 . The driving force T on the car is opposed by a resistive force of 500 N. Calculate T.

A. 300 N

B. 500 N

C. 800 N

D. 1500 N

3. A ball initially at rest, takes time t to fall through a vertical distance h. If air resistance is ignored, the time taken for the ball to fall from rest through a vertical distance 9h is

A. 3t

B. 5t

C. 9t

D. 10t

4. Which one of the following objects is in equilibrium?

A. A stone trapped in the tread of a rotating tire

B. An air molecule as a sound wave passes through the air

C. A steel ball falling at constant speed through oil

D. An electron moving through a metal under the action of a potential difference

5. A machine lifts an object of weight 1.5 x 103 N to a height of 10 m. The machine has an overall efficiency of 20%. The work done by the machine in raising the object is

A. 3.0 x 103 J

B. 1.2 x 104 J

C. 1.8 x 104 J

D. 7.5 x 104 J

6. A rocket is fired vertically. At its highest point, it explodes. Which one of the following describes what happens to its total momentum and total kinetic energy as a result of the explosion?





7. Four cars race along a given race track starting at the same time. The car that will reach the # nishing line # rst is the one with the largest

A. maximum speed

B. acceleration

C. power

D. average speed

8. A lunar module is descending vertically above the lunar surface. The speed of the module is decreasing. Which is a free-body diagram of the forces on the landing module?





9. Which is an example of static friction?

A. ice skating on a frozen pond

B. pushing a box that is at rest

C. braking a car going down a hill

D. driving a car up a hill

10. Using lubricants on engine parts is an example of reducing

A. force

B. friction

C. acceleration

D. motion

A block is placed on a horizontal rough surface. A horizontal force F is applied to the block, as shown below. The force required to keep the block moving at constant speed is less than the force required to make the block move from rest. The explanation for this observation is that

A. before the block moves, the force F must also produce a turning moment

B. a force is not required to keep the block moving at constant speed

C. friction has to be overcome to make the block move

D. the maximum static friction forces are greater than the maximum dynamic friction forces

Number of correct answers: