Dynamics and Space

Velocity and displacementVectors and scalars

Learning Outcomes• Vector and scalar quantities: force, speed,

velocity, distance, displacement, acceleration, mass, time and energy.

• Calculation of the resultant of two vector quantities in one dimension or at right angles.

• Determination of displacement and/or distance using scale diagram or calculation

• Use of appropriate relationships to calculate velocity in one direction.

Lesson 11. Define what is meant by vector and

scalar quantities.2. Describe the difference between

distance and displacement and speed and velocity.

3. Calculate the resultant of two vector quantities at right angles to one another.

Scalar And Vector Quantities

All physical quantities can be divided into two groups – vectors or scalars.

When determining if a quantity is a vector or a scalar you need only ask one question, does direction matter?

• A scalar quantity has size (magnitude) only.• A vector quantity has both size and

direction.

Distance and Displacement

• Distance, d, is how far an object has travelled between two points, regardless of direction.

• It is a scalar and is measured in metres.

• Displacement, s, is the shortest distance travelled between two points in a straight line.

• It is a vector measured in metres and in a particular direction.

Speed and Velocity• Speed and velocity can be calculated by using the following equations:

• Speed = distance velocity = displacement time time

where speed is a scalar and velocity is a vector.

• The direction of the velocity will be the same as that calculated for displacement.

Example 1• A boy walks 40 m north,

then turns back south for 10 m. The journey takes 20 seconds. What is

a) the displacement of the boyb) the distance the boy

travelledc) the average velocityd) the average speed

a) s = 40–10 = 30 m north

b) d = 40 + 10 = 50 m

c) v = s / t = 30 / 20= 1.5 m/s north

d) v = d / t = 50 / 20= 2.5 m/s

Example 2• A car drives 60 km north,

then 80 km east, as shown in the diagram. The journey takes 2 hours. Calculate (in km or km/h):

a) the distance travelledb) the displacementc) the average speedd) the average velocity

a) d = 80 + 60 = 140 kmb) s2 = 802 + 602

s = 100 kmtan Θ = 80 / 60Θ = 530 W of N / (053)

c) v = d / t = 140 / 2= 70 km/h

d) v = s / t = 100 / 2= 50 km/h (053)

NB: The method used for part b) can also be used to work out resultant forces at right angles.

2005

2011

2008

Lesson 21. Define what is meant by vector and

scalar quantities.2. Investigate different quantities to

determine if they are vector or scalar.

3. Identify vector quantities and scalar quantities.

Experiment• You can now carry

out experiments to determine if the following quantities are vectors or scalars:

Vector or scalar?Quantity Predicti

onObservation

MassForceAccelerationTimeEnergy

Examples of Vectors and Scalars

Vectors ScalarsVelocity

DisplacementAcceleration

Force

SpeedDistance

MassTime

Energy (all types)

2005

2008

2009

2010

Lesson 31. Describe how to measure the

average speed of an object.2. Carry out calculations on the above.

Average Speed• The average speed of a body is

found by dividing the total distance travelled by the time of the whole journey.

v = dt

Experiment

Task Distance covered (m)

Time taken (s)

Average speed (m/s)

WalkingYour choice from:Running / hopping / backwards walk etc

• Measure out a distance and record the time taken to travel that distance. Use the results obtained to calculate your average speed in the table below.

How to measure average speed

(3 marks)1. Measure out a distance (½) using a

ruler (½) .2. Record the time taken to travel the

distance (½) using a stopwatch (½).3. Use the equation:

v = dt (1)

2005 Qu: 21

ThinkerDo you know your average speeds?

Lesson 41. Describe how to measure the

instantaneous speed of an object.2. Carry out calculations on the above.

Instantaneous Speed• Instantaneous speed is the speed

of an object at a particular instance in time.

• It is also calculated using v = d / t.• The instantaneous speed is

measured over a very small distance and time period.

Experiment

Measuring Instantaneous Speed

1. Record the length of the mask on the trolley, d, in metres.

2. Release trolley down slope.3. Trolley cuts light gate which then

allows the electronic timer to record time, t, in seconds.

4. Instantaneous speed, v, is calculated using v = d / t.

ExperimentLength of mask = mDistance up slope (m)

Time taken for mask to pass through light gate (s)

Instantaneous speed (m/s)

0.250.500.751.00

2010

2004 Qu:21

SummaryVelocity and displacement

You should now be able to do the following:

• Identify vector and scalar quantities from the following: force, speed, velocity, distance, displacement, acceleration, mass, time and energy.

• Calculate the resultant of two vector quantities in one dimension or at right angles.

• Determine the displacement and/or distance using scale diagram or calculation.

• Use of appropriate relationships to calculate velocity in one direction.