11.1 - Linear Motion

Linear motion is the motion of an object in a straight path.

Distance and Displacement

• Distance: total length of the path travelled by an object.
• Displacement: shortest distance connecting two locations in a specified direction.
• S.I. unit for both quantities: metre (m).

Distance	Displacement
Depends on the entire path travelled.	Depends only on the initial and final positions.
Has magnitude only.	Has magnitude and direction.

For a complete round trip back to the starting point:

• Distance = total length of the whole route.
• Displacement = $0\text{m}$.

Example: two perpendicular paths of $80\text{m}$ each give:

Speed, Average Speed, Velocity and Acceleration

Quantity	Meaning and equation
Speed	Rate of change of distance: $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
Average speed	Rate of change of total distance travelled: $\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$
Velocity	Rate of change of displacement: $\text{Velocity}=\frac{\text{Displacement}}{\text{Time}}$
Acceleration	Rate of change of velocity: $a=\frac{v-u}{t}$

• S.I. unit of speed, average speed and velocity: metre per second (${\text{m s}}^{-1}$).
• S.I. unit of acceleration: metre per second per second (${\text{m s}}^{-2}$).
• In $a=\frac{v-u}{t}$, $a$ = acceleration, $v$ = final velocity, $u$ = initial velocity and $t$ = time taken.
• A positive or negative velocity sign represents the direction of motion.
• Acceleration occurs when velocity increases.
• Deceleration occurs when velocity decreases; its acceleration value is negative.

Solving Numerical Problems

Average-speed example: a $100\text{m}$ runner records $12.58\text{s}$.

Acceleration example: a runner accelerates from rest to $10.44{\text{m s}}^{-1}$ in $9.58\text{s}$.

Ticker Timer and Types of Linear Motion

• A ticker timer produces dots on a ticker tape to study the velocity and acceleration of a moving object.
• The ticker timer vibrates at 50 vibrations per second (50 Hz).
• One tick is the time interval between two adjacent dots.
• A photogate accurately measures very rapid motion or motion over a short time.

• Number of ticks = number of spaces between dots = number of dots $-1$.
• For a five-tick strip, $t=5(0.02)=0.10\text{s}$.

Pattern of successive strips/dots	Type of motion
Equal spacing	Uniform velocity
Spacing increases uniformly	Uniformly increasing velocity (uniform acceleration)
Spacing decreases uniformly	Uniformly decreasing velocity (uniform deceleration)
Irregular spacing	Non-uniform velocity

Activity 11.2: Determining Velocity and Acceleration

Aim: Determine the velocity and acceleration of an object using a ticker timer.

Materials and apparatus: ticker tape, ticker timer, runway, wooden block, trolley, metre ruler and $12\text{V}$ alternating current supply.

1. Set up the apparatus with the runway inclined using the wooden block.
2. Switch on the ticker timer and allow the trolley to move down the runway.
3. Collect the ticker tape and cut it into five strips of 10 ticks each.
4. Arrange the strips side by side to form a ticker-tape chart and record each strip’s length.
5. Calculate the velocity of each strip using $\text{velocity}=\frac{\text{length of strip}}{0.2\text{s}}$.
6. Calculate acceleration using the velocities of strips 1 and 5 and $t=(5-1)(0.2)=0.8\text{s}$.