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Speed, velocity and acceleration
Speed is the rate of change of distance. Speed = Distance / Time ; Average speed = Total distance / Total time
Velocity is the rate of change of displacement. Velocity = Displacement / Time
Acceleration is the rate of change of velocity. Acceleration = (Final velocity - initial velocity) / Time
a = (v - u) / t
Velocity is the rate of change of displacement. Velocity = Displacement / Time
Acceleration is the rate of change of velocity. Acceleration = (Final velocity - initial velocity) / Time
a = (v - u) / t
Displacement-time graph
The shape of the graph gives information on how the object is moving.
If it is a straight line ╱ , the object is moving forward with constant velocity.
If it is a straight line ╲ , the object is moving backward with constant velocity.
If it is a horizontal straight line ▁ , the object is stationary (or at rest).
If it is a curve upwards ╯ , the object is moving with increasing velocity (or acceleration).
If it is a curve ╭ , the object is moving with decreasing velocity (or deceleration).
The gradient of the graph gives the velocity. See the following video on how to calculate velocity from the gradient of graph.
If it is a straight line ╱ , the object is moving forward with constant velocity.
If it is a straight line ╲ , the object is moving backward with constant velocity.
If it is a horizontal straight line ▁ , the object is stationary (or at rest).
If it is a curve upwards ╯ , the object is moving with increasing velocity (or acceleration).
If it is a curve ╭ , the object is moving with decreasing velocity (or deceleration).
The gradient of the graph gives the velocity. See the following video on how to calculate velocity from the gradient of graph.
Velocity-time graph
The shape of the graph gives information on how the object is moving.
If it is a straight line ╱ , the object is moving with constant acceleration.
If it is a straight line ╲ , the object is moving with constant deceleration (or negative acceleration).
If it is a horizontal straight line ▁ , the object is moving with constant velocity (or zero acceleration, a = 0 ms-²).
The gradient of the graph gives the acceleration of the object. See following video on how to calculate the acceleration of an object. In this video, the calculated acceleration is a negative value meaning the object is decelerating for that part of its journey.
**Do note that some students are confused between displacement-time and velocity-time graph. The gradient of displacement-time graph gives the velocity of an object while the gradient of velocity-time graph gives the acceleration of an object.
If it is a straight line ╱ , the object is moving with constant acceleration.
If it is a straight line ╲ , the object is moving with constant deceleration (or negative acceleration).
If it is a horizontal straight line ▁ , the object is moving with constant velocity (or zero acceleration, a = 0 ms-²).
The gradient of the graph gives the acceleration of the object. See following video on how to calculate the acceleration of an object. In this video, the calculated acceleration is a negative value meaning the object is decelerating for that part of its journey.
**Do note that some students are confused between displacement-time and velocity-time graph. The gradient of displacement-time graph gives the velocity of an object while the gradient of velocity-time graph gives the acceleration of an object.
Finding total distance travelled from velocity-time graph
To find total distance travelled, calculate the area under the velocity-time graph.
See the following video on how to calculate the total distance travelled by looking at the area under the velocity-time graph. Please only watch the video until time 4:40 as the last 2 minutes of this video is not relevant to the O level syllabus.
**Do note that finding total distance by looking at area under the graph only applies to velocity-time graph and NOT displacement-time graph! Displacement-time graph already gives the displacement on the y-axis! Lots of common sense has to be used in learning and it never pay well to just blindly memorise things without using common sense or understanding!
See the following video on how to calculate the total distance travelled by looking at the area under the velocity-time graph. Please only watch the video until time 4:40 as the last 2 minutes of this video is not relevant to the O level syllabus.
**Do note that finding total distance by looking at area under the graph only applies to velocity-time graph and NOT displacement-time graph! Displacement-time graph already gives the displacement on the y-axis! Lots of common sense has to be used in learning and it never pay well to just blindly memorise things without using common sense or understanding!
Free fall and air resistance (sky diving example)
Step 1: As a sky diver falls through the air, his velocity increases (or he accelerates). This is because the force of his weight acting downwards due to gravity is greater than force acting upwards due to air resistance.
Step 2: As his velocity increases while falling, the force of air resistance acting upwards also increases. This causes his acceleration downwards to decrease.
Step 3: When the force of air resistance acting upwards increases until it is now equal to his force of weight acting downwards, there is no resultant force on him. His acceleration becomes zero. He falls with constant velocity (also known as terminal velocity is reached).
Step 4: However, this terminal velocity is still quite high and dangerous to land on ground. So the sky diver opens his parachute. This is to increase his surface area in contact with air. Thus, the force of air resistance acting upwards on him suddenly increases as soon as his parachute is opened with a much larger surface area. <NOTE that larger surface area results in higher air resistance acting on the surface>
Step 5: Now, the force of air resistance acting upwards is greater than the force of his weight acting downwards. He falls with decreasing velocity.
Step 6: As his velocity decreases, the force of air resistance acting upwards also decreases. The force of air resistance decreases until it is equal to his force of weight again.
Step 7: Since force of weight downwards equal to force of air resistance upwards, a constant velocity is again reached (also known as terminal velocity). However, this new terminal velocity is much lesser than the first terminal velocity mentioned earlier before he opened his parachute. Landing with this new slower terminal velocity is now safe.
<NOTE also the relationship between velocity and air resistance such that as velocity increases, the air resistance also increases and as velocity decreases, air resistance decreases.>
Step 2: As his velocity increases while falling, the force of air resistance acting upwards also increases. This causes his acceleration downwards to decrease.
Step 3: When the force of air resistance acting upwards increases until it is now equal to his force of weight acting downwards, there is no resultant force on him. His acceleration becomes zero. He falls with constant velocity (also known as terminal velocity is reached).
Step 4: However, this terminal velocity is still quite high and dangerous to land on ground. So the sky diver opens his parachute. This is to increase his surface area in contact with air. Thus, the force of air resistance acting upwards on him suddenly increases as soon as his parachute is opened with a much larger surface area. <NOTE that larger surface area results in higher air resistance acting on the surface>
Step 5: Now, the force of air resistance acting upwards is greater than the force of his weight acting downwards. He falls with decreasing velocity.
Step 6: As his velocity decreases, the force of air resistance acting upwards also decreases. The force of air resistance decreases until it is equal to his force of weight again.
Step 7: Since force of weight downwards equal to force of air resistance upwards, a constant velocity is again reached (also known as terminal velocity). However, this new terminal velocity is much lesser than the first terminal velocity mentioned earlier before he opened his parachute. Landing with this new slower terminal velocity is now safe.
<NOTE also the relationship between velocity and air resistance such that as velocity increases, the air resistance also increases and as velocity decreases, air resistance decreases.>
Solving a typical kinematics question
In this video, there are two formulae used.
For question (a) on finding the final speed of car, the formula used is a = (v - u) / t. The video used another form of this same formula which is v = u + at. You can try to change from one of them to the other form to see for yourself that actually these two forms are just simply the same formula.
For question (b) on finding the distance moved by car, the formula used is distance = average speed X time
d = [(u + v)/2] t
Average speed in this formula is just the average of the initial and final speed (Add initial speed to final speed and divide by 2). Then, multiply average speed to time to get distance. NOTE that this formula only works if the given acceleration in the question is a constant acceleration.
For question (a) on finding the final speed of car, the formula used is a = (v - u) / t. The video used another form of this same formula which is v = u + at. You can try to change from one of them to the other form to see for yourself that actually these two forms are just simply the same formula.
For question (b) on finding the distance moved by car, the formula used is distance = average speed X time
d = [(u + v)/2] t
Average speed in this formula is just the average of the initial and final speed (Add initial speed to final speed and divide by 2). Then, multiply average speed to time to get distance. NOTE that this formula only works if the given acceleration in the question is a constant acceleration.