We shall be looking at motion, the types of motion, and how to solve questions on motion in a simpler way. Let's get right into it.
Motion can be defined as the change of position of a body with timei.e when a body moves from one position to another, it is said to have undergone motion.
Types of motion
- Random motion: This is the movement of a body with no specified direction eg motion of gas particles in air, suspended particles in water etc
- Translational motion: This is the movement of a body from one point to another without rotating. E.g. a car moving from one station to another, a player running from one goal post to another etc
- Oscillatory motion: This is the to and fro movement of a body about a point E.g. a swing, simple pendulum etc
- Rotational motion: This is the movement of a body in a circle about its axis. E.g. rotation of electric fan blades, rotation of the earth about its axis etc
Note: Relative motion is not among the types of motion. Relative motion involves comparing a moving object in relative to a stationary object. For example, when you in a moving car, and you look through the window, it is observed that the trees on the road seems to be moving backwards, but in reality they are stationary. Comparing the motion of the car in relative to the stationary trees is what we call Relative motion.
Basic terms used in motion
- Distance: this is the total length measured between two points. It is measured in metres. Distance is a scalar quantity.
- Displacement: this is the distance travelled in a specified direction. It is also measured in metres. It is a vector quantity.
We are going to use the diagram below to differentiate between distance and displacement.
From the diagram above, it can be seen that a body covered a distance of 10m moving towards the north.
Distance: 10m
Displacement: 10m due North
Let's take some examples on displacement and distance
- In a school compound, a girl walks 40m due east from the laboratory to the staff room to submit her report. Then she turns and walks 30m due north to her classroom. Determine the magnitude of her displacement from the laboratory.
- A man moves 4km southward, then 5 km westward and finally 4km Northward. The displacement of the man is
- A boy travels 12km eastward to a point B and then 5km southwards to another point C. Calculate the difference between the magnitude of the displacement of the boy and the distance travelled by him.
- A lorry travels 10km northwards, 4km eastwards, 6km southwards and 4km westwards to arrive at a point T. What is the total displacement?
- Speed: This describe how fast a body is moving. It is the ratio of distance to time. It is a scalar quantity
- Velocity: This describes the speed of a car in a specified direction. It is the rate of change of displacement. When a graph of displacement is plotted against time, the slope of the graph is called velocity. It is a vector quantity. It is measured in m/s
- Acceleration: A body is said to be accelerating when its velocity is increasing. It is also the rate of change of velocity. it is measured in m/s².
- Deceleration: A body is said to be deccelerating when its velocity is decreasing.
- Constant/ Uniform Velocity: A body is said to be moving at constant velocity if it is neither accelerating or decelerating.
Equations of motion
The equations of motion are :
Where 'v' is called final velocity, 'u' is called initial velocity, 'a' is called acceleration, 's' is called distance
These equations changes when you are dealing with a body moving vertically. They are:
Note the following.
- When the body is moving against gravity, ( i.e going up) the positive sign changes to negative sign. You will have this
- When the body is at rest, initial velocity is zero ( i.e u=0)
- When a body is thrown upward, at the maximum height, final velocity is zero (i.e V= 0)
Let's take some examples
- The type of motion the wheels of a moving car undergo is translational and rotational motion.
- When a ball rolls on a smooth level ground, the motion of its center is translational.
- A Cylinder rolling down an inclined plane undergoes translational and rotational motions.
- During the same interval, it is observed that a train travels the same distance as does a lorry. The two vehicles therefore have the same Average speed
- A car starts from rest and moves with a uniform acceleration of 30m/s² for 20s.Calculate the distance covered at the end of the motion.
- A car moves with an initial velocity of 25m/s and reaches a velocity of 45m/s in 10s. What is the acceleration of the car?
- If it takes an object 3s to fall freely to the ground from a certain height, what is the distance covered by the object?[g = 10m/s²]
Solution
- A bullet fired vertically upwards reaches a height 500m. Neglecting air resistance. Calculate the magnitude of the initial velocity of the bullet (g = 10 m/s²)
Solution
In this question, the bullet is moving against gravity. Also, at the maximum height, V= 0m/s, H=500m, u = ?
Velocity- time graph
Velocity-time graph shows the relationship between velocity of a body and the time it takes to cover a certain distance.
The velocity-time graph has three stages; they are the acceleration stage (S1), the constant velocity stage (S2) and the deceleration stage (S3).
The area under the velocity-time graph is called distance while the slope of the graph is called acceleration. We are going to be looking at questions on velocity- time graph
- From the diagram above, the region of zero acceleration is NS
- The diagram above shows a velocity-time graph. The statement that is true about this motion is that the car has no acceleration between point F and G
- From the velocity-time graph below, determine the total distance covered.
The total distance covered can be calculated in two ways.
First method
Second method
Which ever you prefer, your choice.
- What is the acceleration between two points on a velocity-time graph which has coordinates (10s, 15m/s) and (20s, 35m/s)?
- A train with an initial velocity of 20m/s is subjected to a uniform deceleration of 2m/s² the time required to bring the train to a complete halt is?
In this question, the body is said to be decelerating, when it got to a complete halt, V =0
- A ball is thrown vertically into the air with an initial velocity u. What is the greatest height reached?
Exercises
From the velocity-time graph shown above, which of the following quantities CANNOT be determined?
(a) Total distance travelled (b) Deceleration (c) Initial acceleration (d) Initial velocity
2. A car accelerates uniformly from rest at 3m/s², its velocity after travelling a distance of 24m is
3. A bus travelling at 15m/s accelerates uniformly at 4m/s² What is the distance covered in 10sec? (a) 150m (b)170m (c)350m (d)600m
4. Which of the following phenomenal is the practical evidence for the existence of the continual motion of molecules?(a) translational motion(b)Rotational motion(c) Brownian motion(d) Oscillatory motion