3.1 Speed, Velocity and Acceleration

3.1.1 Speed, Velocity and Acceleration 

Speed 

Speed is how fast an object is moving. In other words, the distance covered by a body in unit time is called its speed.

It is a scalar quantity because it has no direction

• Formula: Speed = \( \frac{distance}{time} = \frac{d}{t} \)
• Units: The unit for speed is meters per second \( \frac{m}{s} \).

Example 1: Speed

• Scenario: A car travels a distance of 200 meters in 40 seconds.
• Calculation: Speed = \( \frac{distance}{time} = \frac{200m}{40s} \) = 5 \( \frac{m}{s} \)
• Interpretation: The speed of the car is 5 meters per second.

Average Speed:

Average speed is the total distance traveled by an object divided by the total time taken.

• Average speed is when the speed of a moving object does not remain constant.

For example: Acceleration makes the body faster, while deceleration makes it slower; in both cases, speed is not constant.

Average speed is the total distance traveled by an object divided by the total time taken.

• Formula: Average Speed = \( \frac{TotalDistance}{TotalTime} \)
• Units: Like speed, the unit for average speed is typically meters per second \( \frac{m}{s} \) in the SI system.

Example: Average Speed

• Scenario: A car travels 300 kilometers in 5 hours.
• Calculation:
• Interpretation: The average speed of the car over the entire journey is 60 kilometers per hour.

❓ Exam Question 

0625/0972/22-Feb-Mar-2021-Q3

A train begins a journey from a station and travels 60 km in a time of 20 minutes.
What is the average speed of the train? 

❓ Exam Question

1524-j21-22-2021-Q2

An aeroplane flies from town X to town Z, stopping for 1 hour at town Y to pick up more

passengers. The distances between the towns are shown.

The total time taken between leaving X and arriving at Z is 3 hours.

What is the average speed of the aeroplane in the air? 

Velocity

Velocity is how fast an object is moving in a specific direction. In other words, It is the displacement of a body per unit

• Formula:  Velocity =\( \frac{Displacement}{Time} \) =\( \frac{S}{t} \)
• Units:  unit for velocity is meters per second \( \frac{m}{s} \).

Example : Velocity

• Scenario: A cyclist moves 150 meters east in 30 seconds, find Velocity?
• Calculation:   ​= 5 m/s (east)
• Interpretation: The velocity of the cyclist is 5 meters per second to the east.

Speed and Velocity 

Displacement and Velocity – How is it different from Distance and Speed? | Physics

Related questions

• How the distance differs from displacement?
• Differentiate between speed and velocity.
• Does speed include distance or displacement?
• Does velocity include distance or displacement?

Acceleration 

Acceleration is rate of change of velocity of the body.

• Acceleration (a) is a vector quantity
• Acceleration has both magnitude and direction.
• Formula: $\text{Acceleration}=\frac{\text{Change in Velocity}}{\text{Time}}$​$=\frac{\text{Δv}}{\text{Δt}}$$=\frac{\text{v – u}}{\text{t}}$
• Units: The SI unit for acceleration is meters per second squared ($\frac{\text{m}}{\text{s²}}$).

Example : Acceleration

• Scenario: A car increases its speed from 10 m/s to 30 m/s in 5 seconds.
• Calculation: $\text{Acceleration}=\frac{\text{Change in Velocity}}{\text{Time}}=\frac{(30\text{m/s}-10\text{m/s})}{5\text{s}}=4{\text{m/s}}^2$
• Interpretation: The car is accelerating at a rate of 4 meters per second squared.

Important Points

• Positive acceleration means the velocity of a body is increasing over time.
•  For example, a rocket accelerating in space with a value of a = 25 $\frac{\text{m}}{\text{s²}}$ signifies a continuous increase in its velocity.
• Negative acceleration occurs when the velocity of a body decreases over time, indicating deceleration or slowing down. 
• For example, a car with an acceleration of a = -7 $\frac{\text{m}}{\text{s²}}$ is slowing down.

Example 1:

 A train accelerates at 12 $\frac{\text{m}}{\text{s²}}$ for 8 s. If its initial velocity is 5 $\frac{\text{m}}{\text{s}}$, what will be the final velocity?

Solution:

• a = 12$\frac{\text{m}}{\text{s²}}$
• u = 5$\frac{\text{m}}{\text{s}}$
• t = 8s

By using formula, a $=\frac{\text{Δv}}{\text{Δt}}$

• ∆v = a × ∆t 
• ∆v    = 12×8 
• ∆v    = 96$\frac{\text{m}}{\text{s}}$

And                            

• ∆v  =  v  –  u
• v =  ∆v + u 
• v  =  96 + 5

v    = 101$\frac{\text{m}}{\text{s}}$

Example 2:

A car accelerates along a straight road from rest to  85 $\frac{\text{m}}{\text{s}}$ in half a minute. What is the magnitude of its average acceleration?

Solution:

• t = 30 s
• u = 0 $\frac{\text{m}}{\text{s}}$
• V = 85 $\frac{\text{m}}{\text{s}}$

By using formula,

a$=\frac{\text{Δv}}{\text{Δt}}$$=\frac{\text{v – u}}{\text{t}}$$\frac{}{}$$=\frac{\text{85 – 0}}{\text{30}}$  

a    =  2.8 $\frac{\text{m}}{\text{s²}}$