1.2 Speed, Velocity, Acceleration, and Motion Graphs
CIE IGCSE PHYSICS
1.2 MOTION
SPEED:
Speed is defined as the distance travelled per unit time.
The units for speed and velocity are m/s or km/h. To measure speed, we use the formula:
Speed = Distance Travelled
Time Taken
Example:
Think about being a passenger in a car travelling at 90km/h. This means that the car travels 90km every hour. In 1 second, how far does the car go?
1 hour = 60 minutes
1 min = 60 secs
1 sec = 90
60x60
= 90
3600
= 0.025 km
1km = 1000 m
0.025km = 1000 x 0.025
90 km/h = 25m/s
Calculate the speed of a car that travels 500 meters in 20 seconds.
S = D/T
S = 500/20
S = 25 m/s
A cyclist has an average speed of 5m/s for 2 minutes. Calculate the total distance travelled.
1 min = 60 secs
2 min = 120 secs
Total distance = S x T
= 5 x 120
= 600 m
VELOCITY:
Velocity, on the other hand, is the speed in a given direction.
To measure velocity, we use the formula:
Velocity = Displacement / Time
NOTE:
If the speed of an object is changing, then the object is accelerating or decelerating.
In this case, speed will be measured as an average.
Average Speed = Total Distance Travelled / Total Time
The difference between speed and velocity:
The velocity of an object is one piece of information, but it consists of two parts: the speed and the direction.
For example, when a space rocket is launched, it is likely to reach a speed of 280m/s after 30 seconds.
280 m/s is its speed but 280 m/s upward is its velocity.
A velocity can have a minus sign. This means that the object is travelling in the opposite direction.
Example:
The journey to school is about 10 km. It takes 15 minutes by car. Calculate its average speed.
Average speed = Total distance travelled
Total time taken
= 10000
900
= 11 m/s
A person walks at an average speed of 0.5 m/s and travels a total distance of 1500m. Calculate the time taken.
Time taken = Total distance
Average
= 1500
0.5
= 3000 s
ACCELERATION:
An object is said to be accelerating as its speed increases with time.
Acceleration is the change in velocity per unit time or rate of change of velocity.
It can also be referred to as the rate at which an object speeds up.
The units for acceleration are m/s2. To measure acceleration, we use the formula:
Acceleration = Change in velocity
Change in time
The opposite of acceleration is called deceleration. This is a term that is used when the speed of an object decreases with time.
Example:
A car is travelling in a straight line. The speed of the car changes from 25 m/s to 15 m/s in a time of 2 seconds. Calculate the value of the acceleration of the car.
a = Change in velocity per unit time in meters per second squared
V - U
T
Change in time
a = 15 - 25
2
a = - 10
2
a = - 5 m/s
MOTION GRAPHS:
1) Velocity-Time Graphs
A velocity-time graph illustrates how an object's velocity changes over time.
The horizontal axis shows time, while the vertical axis shows velocity.
A horizontal line represents constant velocity, while a sloped line indicates acceleration (upward slope) or deceleration (downward slope).
A steeper slope means a greater rate of acceleration.
When the line crosses the horizontal axis, the object changes direction.
The area under the curve represents displacement, showing how far the object has traveled.
2) Displacement -Time Graphs
These are also known as Distance -Time Graphs.
A displacement-time graph shows how the position of an object changes over time.
The horizontal axis represents time, and the vertical axis shows displacement from a fixed starting point.
A straight, sloped line indicates constant velocity—the steeper the slope, the faster the object is moving.
A horizontal line means the object is stationary.
A curved line shows changing velocity, meaning the object is accelerating or decelerating.
If the line returns toward the horizontal axis, the object is moving back toward its starting point.
The table below shows how the motion of an object can be described from the shape of the distance-time graph
State of the object | Shape of the distance-time graph |
At rest | Horizontal Line |
Moving at a constant speed | Straight line of positive gradient |
Acceleration | Curve with increasing gradient |
Deceleration | Curve with decreasing gradient |
Falling Objects:
When you drop an object, it falls towards the ground. The force of gravity acts on the object and causes it to accelerate.
The acceleration due to gravity, also known as the acceleration of free fall (g), acts downwards and has an approximate value of 9.8m/s2.
This is with the assumption that frictional forces are negligible.
In a vacuum, all objects have a free-fall acceleration. If a heavy object together with a light object are both released in a vacuum from the same height, they will reach the bottom at the same time.
Terminal Velocity:
When a skydiver jumps from a plane, the weight will be much greater than the opposing force.
The skydiver’s speed increases rapidly, and so does the resistive force.
When he opens his parachute, the resistive force will suddenly be greater than his weight.
After some time, the resistive force will balance with his weight, and he will move steadily up to the ground with a value of speed called Terminal Velocity.
Written by: Noella Gracious
Edited by: Yassein Abdoun