National 4 & 5 Physics Portree High School
Dynamics & Space 1 – Summary Notes
Speed and acceleration
Speed and acceleration are two different things.
Any moving object has a speed. ‘The girl cycled at 10 metres per second’ – this is a speed.
A word about units of measurement…
If the distance is in metres and the time in seconds, speed is measured in metres per second. This is
abbreviated to
ms-1. Use this unit for speed in Nat 4 & 5 and you won’t go far wrong.
When working on problems with speed, time and distance we use the well known formula:
Example:
Calculate the speed of an arrow that takes 3s to travel 600m.
V=?
v = d/t = 600/3 = 200ms-1
t = 3s
d = 600m
When talking about speed we need to know if we’re dealing with AVERAGE or INSTANTANEOUS
speed.
The INSTANTANEOUS speed is an objects’ speed at a particular moment in time; look at the
speedometer of a car and that will tell you the instantaneous speed of the car at that time.
The AVERAGE speed of an object is the speed taken over the entire journey, and will almost certainly
be different to the instantaneous speed. To work out average speed, you need the total distance
travelled and the total time take. Average speed is given the symbol
(spoken as “v bar”).
National 4 & 5 Physics Portree High School
Acceleration
If an object is accelerating, its speed is changing. So, if an object is speeding up, or slowing down, it
is said to be accelerating. Acceleration can be calculated using the formula:
Acceleration is measured in ‘metres per second per second’ or ms-2.
Speed – time graphs can be used to show an object’s motion:
Speed – time graphs can be used to calculate acceleration:
Initial speed, u = 5 ms-1
Final speed, v = 8 ms-1
Time, t = 12 s
a = (v – u)/t
= (8 – 5)/12
= 3/12 = 0.25 ms-2
It is very easy to get this type of calculation wrong. Pupils sometimes get the initial and final speeds
mixed up. There is also the risk of trusting the calculator too much; you need to work out the top
(numerator) of the formula first and then divide by t.
For example, if you put 8 - 5 / 12 into a calculator, it will give you the answer of 7.583, which is
wrong! Calculators perform division first, then subtraction second - this is clearly not what you
want, so please be aware!
National 4 & 5 Physics Portree High School
Speed – time graphs can be used to work out the distance travelled, by calculating the area ‘under
the graph’:
The area ‘under the graph’ is the area between the
x-axis, y axis and red line. This can be split into a
triangle (1) on top of a rectangle (2).
Area (1) = ½ b x h = ½ x 12 x 3 = 18m
Area (2) = 12 x 5 = 60m
Total area, and total distance travelled = 18 + 60 = 78m
Scalars and Vector
A scalar is a physical quantity that has a magnitude (size) only. A vector is a physical quantity that
has magnitude and direction.
Speed and distance are SCALAR quantities, having only a magnitude.
Velocity and displacement are VECTOR quantities having both magnitude and direction.
When you are asked to calculate the displacement or velocity of an object, then you need to
determine the magnitude and the direction.
Example:
A person walks 100m due west then turns and walks 60m due east, all in a time of 80s.
(a)
(b)
(c)
(d)
Calculate their distance travelled.
Calculate their average speed.
Calculate their displacement.
Calculate their velocity.
Distance travelled
This is the total distance travelled, and is 100 + 60 = 160m
Average speed
This is speed = distance/time. V = d/t = 160/80 = 2ms-1
Displacement
Displacement is the term given to where they finished compared with where they started.
Velocity
Velocity is calculated using velocity = displacement / time = 40 / 80 = 0.5ms-1
National 4 & 5 Physics Portree High School
Velocity – time graphs can be used to describe an object’s motion, being particularly useful when an
object’s motion changes direction. The displacement of an object can be calculated by working out
the area under the graph, taking direction into account.
Consider the example of a ball thrown up in the air. Motion upwards is positive, motion downwards
is negative:
Adding Velocities
It is quite common in the real world, to have two separate velocities acting on one object. The
overall, or RESULTANT, velocity can be found by adding the two velocities, taking into account
direction.
For example, an aircraft flying due north at 100ms-1 has a wind of 20ms-1 blowing it due south. These
two velocity vectors can be added ‘nose to tail’, to work out the RESULTANT velocity of the aircraft:
Two velocities at right angles to each other can be combined using Pythagoras.
For example, a swimmer swims across a river at a velocity of 4ms-1. The river current forcing the
swimmer downstream is 3ms-1. Find the resultant velocity of the swimmer.
The resultant velocity of the swimmer is
5ms-1 at an angle of 370 downstream.
National 4 & 5 Physics Portree High School
Newton’s Laws of Motion
Force is measured in Newton’s (N). A force can change the shape, speed and direction of an object.
Newton’s First law states:
An object will remain at rest, or move with a constant speed in a straight line if the forces acting on it
are balanced.
Newton’s Second Law of motion :
This deals with unbalanced forces. If the forces acting on an object are unbalanced, then that object
will accelerate.
Example:
What unbalanced force is needed to accelerate a mass of 6Kg by 4ms-2?
F=?
a = 4ms-2
F = ma = 6 x 4 = 24 N
m = 6Kg
Sometimes, more than one force is involved, and we need to find the total unbalanced force before
we can find the acceleration.
Example: Calculate the acceleration of the following bob:
Total unbalanced force = 140 – 20 = 120 N
a= ?, m = 50Kg, F = 120N, a = F/m = 120/50 = 2.4ms-2
National 4 & 5 Physics Portree High School
Newton’s Third Law
Forces act in pairs – for every action force there is a reaction force.
The man pushes against
the wall with a force of 100N.
The wall pushes back with an
equal and opposite
force of 100N.
Weight and Mass
Mass is how much matter (or ‘stuff’) an object is made up of, measured in Kg. An object’s mass
doesn’t change unless bits are taken off or added on.
Weight is the force due to gravity acting on a planet, measured in N. The weight of an object
depends on where it is in the universe. In some locations there will be a large gravitational field
strength, causing a large weight, and in other locations, an object will be almost ‘weightless’ due to a
low gravitational field strength.
Mass and weight are connected by the formula:
This table can be used to find the
gravitational field strength on a particular
planet in our solar system.
Example:
Calculate the weight of a 2Kg hammer on the moon.
W=?
m = 2Kg
g = 1.6 N/Kg (on the moon)
W = mg = 2 x 1.6 = 3.2 N
National 4 & 5 Physics Portree High School
Work Done
Work done is a form of an energy and is measured in Joules (J).
Example:
Calculate the work done when a strong man pulls a truck with a force of 700N a distance of 20m.
Ew = ?
F = 700N
D = 20m
Ew = Fd = 700 x 20 = 14200J