Understanding kinematics, particularly concepts like speed and velocity, forms a crucial foundation in the study of physics. As students gearing up for their GCE O Level Physics exam, grasping these principles is not only essential for academic success but also for unlocking a deeper appreciation of the world around us. In this article, we will delve into the fundamentals of kinematics, exploring how speed and velocity shape our understanding of motion and dynamics. 

 

Exploring Speed and Velocity in Kinematics

In the study of kinematics, speed and velocity are crucial concepts that describe how objects move through space.

Speed is defined as the magnitude of the rate of motion of an object, specifically as the distance travelled per unit of time. It is a scalar quantity, meaning it only specifies how fast an object is moving without regard to direction. The standard unit of speed is metres per second (m/s).

Velocity, on the other hand, is defined as the rate of change of displacement over time. It is a vector quantity, meaning it not only specifies the speed of an object but also includes its direction of motion; velocity has both magnitude (speed) and direction. Similar to speed, velocity is also measured in metres per second (m/s).

 

Calculating Speed 

Average speed can be determined using the formula: Distance Travelled / Time Taken.

Let’s work through an example to calculate James’ average speed:

 

James runs once around a 0.25km track in 2.0min and returns to his starting position. What is the magnitude of his average speed?

Velocity 1

 

Checkpoint! Now, you give the following question a try!

Speed Question 1: A police car accelerates quickly to 60 metres per second in order to pursue a motorcycle that is recklessly speeding at 45 metres per second. How long will it take the police car to catch up if the motorcycle is 600 metres ahead of the police car at the beginning of the chase?

 

Check your Answers! Did you get it right?

Kinetics 2

 

Calculating Acceleration using Velocity

Acceleration quantifies how much an object’s velocity changes over time. The value of an acceleration can be calculated using Change in Velocity / Time Taken.

 

Uniform Acceleration

Uniform acceleration specifically describes a scenario where an object’s speed (velocity) increases or decreases at a constant rate over equal time intervals. For example, if an object increases its velocity by 5 metres per second every second, it is experiencing uniform acceleration. 

 

Let’s put this concept into perspective by working on this example question below:

Determine the acceleration of a body whose velocity changes from 2.50m/s to 6.75m/s in 3.0s.

Velocity 3

 

Checkpoint! Now, you give the following question a try!

Velocity Question 1: At time t = 1 min, Bobby’s race car is travelling at a velocity of 20 metres per second. At time t = 2 min, the race car reaches a velocity of 40 metres per second. What is the average acceleration of Bobby’s race car?

 

Check your Answers! Did you get it right?

Kinetics 5

 

Non-uniform Acceleration

On the other hand, non-uniform acceleration occurs when the speed (velocity) of an object changes by varying amounts over equal time intervals.

Some characteristics of non-uniform acceleration include:

  1. The acceleration, which represents the change of speed over time, is not constant ; The fluctuation in speed causes the speed of the object to change by different amounts during each successive interval of time.
  2. The variability in acceleration leads to complex motion patterns where the speed of the object changes unpredictably as time progresses; irregular changes in speed over time.

 

Graphs that You Must Know

Understanding these graphs helps in visualising and analysing the motion characteristics of objects under different conditions, whether stationary, moving at a constant velocity, or undergoing constant acceleration, and how these relate to their speed over time.

 

Stationary

Velocity 5

Interpretation of the above two graphs
Displacement-time Graph

  • The object remains at rest throughout the time interval.
  • There is no change in position (displacement).
Velocity-time Graph

  • The object remains at rest throughout the time interval.
  • There is no change in speed (velocity).

 

Uniform Motion (Constant Velocity)

Kinematics 6

Interpretation of the above two graphs
Displacement-time Graph

  • The displacement-time graph shows a steady increase in position over time.
Velocity-time Graph

  • The velocity-time graph shows a flat line at a constant positive value, indicating the uniform velocity of the object.

 

Motion with Constant Acceleration

Velocity 7

Interpretation of the above two graphs
Displacement-time Graph

  • The object’s velocity changes uniformly over time due to constant acceleration.
  • Displacement increases at an increasing rate as time progresses.
Velocity-time Graph

  • The object’s velocity changes uniformly over time due to constant acceleration.
  • Velocity changes linearly over time due to constant acceleration.

 

Checkpoint! Now, you give the following question a try!

Graph Question 1: The velocity-time graph of a car in motion is shown below. What is the total displacement travelled by the car? (Answer in terms of X and Y)

Kinematics 8

 

Check your Answers! Did you get it right?

Total Displacement = Area X – Area Y

 

Understanding Free Fall and its Velocity

Understanding the following phases of free fall and terminal velocity is essential in physics as it illustrates how gravitational acceleration and air resistance interact to determine the speed and motion of objects falling through Earth’s atmosphere.

When an object falls freely near the Earth’s surface, its motion is governed by gravitational acceleration and air resistance, leading to the following phases:

 

(1) Constant Acceleration Phase

  • The acceleration of a free falling object near to the Earth is constant at 10m/s2.
  • When an object is in free fall, it experiences negligible air resistance, thus the speed of the object increases at a constant rate of 10m/s2.
  • This means that the object’s speed increases by 10m/s every second.

 

(2) Uniform Acceleration Phase

  • Initially, air resistance is negligible when the object begins its descent.
  • However, the object would begin to accelerate uniformly due to gravity, thus resulting in a continuous increase in speed.

 

(3) Terminal Velocity

  • As the object falls through the air over a longer distance, air resistance gradually increases. 
  • Eventually, the force of air resistance matches the gravitational force (weight) of the object.
  • At this point, the resultant force acting on the object becomes zero, leading to no further acceleration.
  • The object then descends at a constant speed, also known as terminal velocity.

 

This can also be expressed in terms of graphs, as follows:

Velocity 9

 

Looking for a visual aid to enhance your understanding of free fall and its connection to velocity? Watch this video!

 

Checkpoint! It’s time to test your understanding of the topic!

A ball falls towards the ground, first in the air and then later in an evacuated tube, which has most of the air in it removed. Which graph shows the velocity of the ball changes with time in these cases?

Kinematics 10

 

Check your Answers! Did you get it right?

Check your answers with Teacher Manpreet here! Did you get it right? And if not, were you able to catch Teacher Manpreet’s explanations on how to identify the graph which accurately portrays the velocity of the ball changes with time?

 

Ready to dive deeper into the exciting world of physics? 

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