Describe concepts of linear motion (speed, velocity, acceleration, distance, and displacement)

Distance is the total length of the path traveled by an object from one point to another. It tells us how far an object has moved but does not indicate the direction. Distance is a scalar quantity, meaning it has only magnitude (size) but no direction.

• Symbol: s or d
• SI Unit: metre (m)
• Example: If a student walks 200 m from home to school, the distance traveled is 200 m.

Displacement is the shortest distance between the initial and final positions of an object in a specific direction. It is a vector quantity, meaning it has both magnitude and direction.

• Symbol: s or d
• SI Unit: metre (m)
• Example: If the student walks 200 m east from home to school, the displacement is 200 m east.

Key Difference

Important: If an object returns to its starting point, the distance traveled is greater than zero, but the displacement is zero.

Speed is the rate of change of distance. It tells us how fast an object is moving without considering the direction. Speed is a scalar quantity.

$Speed = \frac{\text{distance}}{\text{time}}$

$v = \frac{s}{t}$

Where:

• v = speed (m/s)
• s = distance (m)
• t = time (s)

SI Unit: metres per second (m/s)

Example: A cyclist covers 300 metres in 60 seconds. What is the speed?

$Speed = \frac{300 \, \text{m}}{60 \, \text{s}} = 5 \, \text{m/s}$

Velocity is the rate of change of displacement. It tells us how fast an object is moving and in which direction. Velocity is a vector quantity.

$Velocity = \frac{\text{displacement}}{\text{time}}$

$v = \frac{s}{t}$

Where:

• v = velocity (m/s)
• s = displacement (m)
• t = time (s)

SI Unit: metres per second (m/s)

Example: A car moves 100 metres north in 20 seconds. What is the velocity?

$Velocity = \frac{100 \, \text{m}}{20 \, \text{s}} = 5 \, \text{m/s \, north}$

Difference Between Speed and Velocity

Uniform velocity occurs when an object moves equal displacements in equal time intervals. If an object changes its velocity (increases or decreases), it is accelerating.

Acceleration is the rate of change of velocity. It describes how quickly an object's velocity changes over time. Acceleration is a vector quantity.

$Acceleration = \frac{\text{change in velocity}}{\text{time}}$

$a = \frac{v - u}{t}$

Where:

• a = acceleration (m/s²)
• v = final velocity (m/s)
• u = initial velocity (m/s)
• t = time (s)

SI Unit: metres per second squared (m/s²)

Types of Acceleration

1. Positive acceleration: Velocity increases with time (speeding up)
2. Negative acceleration (deceleration/retardation): Velocity decreases with time (slowing down)
3. Zero acceleration: Velocity remains constant (uniform velocity)

Example: A motorbike increases its velocity from 5 m/s to 25 m/s in 10 seconds. Calculate the acceleration.

$a = \frac{25 \, \text{m/s} - 5 \, \text{s}}{10 \, \text{s}} = \frac{20 \, \text{m/s}}{10 \, \text{s}} = 2 \, \text{m/s}^2$

This means the motorbike's velocity increases by 2 metres per second every second.

A bodaboda (motorcycle taxi) starts from rest at Dar es Salaam and accelerates at 2 m/s² for 5 seconds.

Calculate:

1. The final velocity after 5 seconds
2. The distance traveled in this time

Solution:

1. Using $v = u + at$

   • Initial velocity, u = 0 m/s (starts from rest)
   • Acceleration, a = 2 m/s²
   • Time, t = 5 s
   • $v = 0 + (2 \times 5) = 10 \, \text{m/s}$

2. Using $s = ut + \frac{1}{2}at^2$

   • $s = 0 + \frac{1}{2} \times 2 \times 5^2$
   • $s = \frac{1}{2} \times 2 \times 25 = 25 \, \text{m}$

The bodaboda travels 25 metres in 5 seconds and reaches a velocity of 10 m/s.

In Tanzania, understanding linear motion is essential for traffic safety and transportation. When a daladala (minibus) stops at a bus stop, the driver must estimate the braking distance needed to stop safely based on the vehicle's velocity and acceleration. Similarly, bodaboda riders use these concepts when navigating through busy streets in Dar es Salaam or Arusha, adjusting their speed and acceleration to avoid accidents and maintain safe following distances from other vehicles.