(Not completed!) Chapter 2: Motion in a straight line

Scalars vs. Vectors → what’s the difference?

• A scalar is a measurement that only has magnitude (size), but no particular direction. Some examples are:

  • Speed

  • Distance

  • Temperature

  • Volume

  • Mass

  • Energy

• A vector is a quantity that has both direction and magnitude. Some examples are:

  • Velocity

  • Displacement

  • Weight (force due to gravity)

  • Momentum

Distance vs. displacement → what’s the difference?

• Distance (s) - is the length between two points

• Displacement (s^→) - is the position of an object relative to the origin or starting point. It must be given a positive or negative value to show which side of the origin the object is positioned. It has both direction and magnitude, and therefore is a vector quantity

  • For example: if a marathon of 42.2km starts and finishes at the same line, distance = 42.2, where as displacement = 0.

• Both distance and displacement are measured in S.I. unit: metres (m)

Distance-time graphs and how to read them

Displacement-time graphs and how to read them

Movement and time intervals

• Movement is measured as the change of position in the time interval

• The time interval is shown as Δt, there Δt = t(final) - t(initial)

  • It represents the amount of time that has passed from one measurement to the next

  • The unit of measurement for time is seconds (s)

Speed vs. velocity → what’s the difference?

• Speed (v) - is the distance covered in a time interval.

  • It is a measure of how fast something is travelling. It can be measured by observing the distance travelled and dividing by the observed time taken.

  • Formula: v = s/t

• Velocity (v^→) - is the change in displacement in the time interval, and therefore is a vector quantity.

  • Speed is the magnitude of the velocity

  • Velocity also includes direction

Speed-time graphs and how to read them

Average speed vs. instantaneous speed - what’s the difference

• Average speed is the one single speed that would enable an object to cover a specified distance in a given time interval.

  • Formula: v(avg) = s/Δt

  • Where the average speed = distance/Δtime

• Instantaneous speed is the rate at which distance is covered over a time interval that is so brief as to be negligible.

  • For example: a car’s speed at a certain moment is its instantaneous speed. If the time interval was very small, the average speed becomes very close the the instantaneous speed.

  • So if t = low, v(inst) ≈ v(avg)

Relative velocity

• Relative velocity depends on the frame of reference

• Formula: velocity(observer) - velocity(other object)

  • If objects are travelling in opposite directions, the velocity(observer) - velocity(other object) will necessarily yield a positive number.

  • Whether they are

    closing or separating will depend on their initial positions, but the relative velocity will have the same

    magnitude.

Velocity-time graphs and how to read them

Acceleration vs. deceleration

• The both involve a change in speed over time; Δvelocity/Δtime.

• Acceleration is the positive change of velocity over time, this means that the velocity is increasing.

• Deceleration is the negative change of velocity over time, this means that the velocity is decreasing.

• a(avg) = Δv/Δt

• Acceleration is measured in m/s/s/ or ms^-2