Linear Motion
All motion is relative.
If unstated, the motion mentioned is relative to the surface of the Earth.
Even things that are at rest are moving.
You’re moving at 170,000 km/h right now.
Before Galileo, people described things as either slow or fast.
Galileo was the first to measure speed.
Speed = Distance/Time
Galileo measured distance easily. He struggled with measuring time.
Sometimes he used his own pulse, or dripping water drops.
Eg: Cyclist covering 16 meters in 2 seconds has a speed of 8 meters per second (m/s).
Instantaneous speed is the speed of an object at any instant.
If a car travelled at 50 km/h for an hour, it would cover 50 km. If it travelled for half an hour, it would cover 25 km.
Average speed = total distance covered/time interval
Eg: if you travel 320 km in 4 hrs, the average speed is 80 km/h.
Average speed doesn’t tell you the different speeds at smaller time intervals.
Average speed is different from instantaneous speed.
Total distance covered = average speed x time interval
The speed and direction of motion for an object gives us its velocity.
Speed → car travelling at 60 km/h.
Velocity → car moving at 60 km/h towards north.
Speed is how fast an object moves.
Velocity is how fast an object moves and in what direction it moves.
Vector quantity: Quantity that specifies magnitude and direction.
Scalar quantity: Quantity that specifies only magnitude.
Constant speed is steady speed.
Constant velocity is constant speed and constant direction.
Constant direction means the object moves in a straight line. The path doesn’t curve.
Constant velocity → Motion in a straight line at a constant speed.
Velocity changes if speed or direction or both change.
Velocity of an object changes with a change in speed, change in direction, or change in both.
Acceleration → How quickly the velocity changes and in what direction.
Formula → Acceleration = change of velocity/time interval
Acceleration is defined by change.
Eg: increasing velocity from 30 km/h to 35 km/h in one second, to 40 km/h in the next, 45 km/h in the next, and so on.
Here, the acceleration is 5 km/h.s
Acceleration is the change per second in the velocity.
Acceleration is the increase or decrease in the velocity.
Deceleration → When there is a large decrease per second in the velocity.
When we move in a curved path, our direction is constantly changing, so we are accelerating, even if we are moving at a constant speed.
Eg: Standing in a moving bus. When a bus moves at a constant velocity, you can stand with no extra effort. When the bus accelerates, you experience difficulty standing.
Galileo demonstrated acceleration using experiments on inclined planes.
A ball rolling down an inclined plane picks up the same speed with each successive second. This is constant acceleration.
Eg: For a ball rolling down a plane inclined at an angle, let’s say it picks up a speed of 2 m/s with each second.
The instantaneous velocity at 1s intervals at this acceleration is 0, 2, 4, 6, 8, 10 m/s, and so on.
Velocity acquired = acceleration x time
At the end of 1s, the ball travels 2 m/s, at the end of 2s, it is travelling 4 m/s, at the end of 10s, it’s 20 m/s.
Acceleration down an incline is constant for each incline.
Steeper inclines have greater accelerations.
When the incline is tipped vertically, the ball accelerates to its highest extent. It falls with the acceleration of a falling object.
When air resistance can be ignored, all objects fall with the same acceleration.
When an object falls under the influence of only gravity, it is in a state of free fall.
There’s no other restraints like friction with the air acting on the object.
Instantaneous velocity of a free falling object at 1 second intervals:
Time of Fall (s) | Velocity Acquired (m/s) |
|---|---|
0 | 0 |
1 | 10 |
2 | 20 |
3 | 30 |
4 | 40 |
5 | 50 |
t | 10t |
During each second, the object gains a speed of 10 m/s.
Gain per second is the acceleration.
Free fall acceleration = 10 m/s^2.
For free falling objects, g represents acceleration.
Acceleration is due to gravity.
g is slightly different on the surface of the Moon and the surfaces of other planets.
Average value of g = 9.8 m/s2
Instantaneous velocity, v = gt
Speedometers can be used to measure free fall acceleration.
For an object thrown upwards:
It slows down as it moves upwards.
At its highest point, it changes direction.
At its highest point, its instantaneous speed becomes 0.
When it starts moving downwards, it acts like its been dropped from rest at that height.
Upward deceleration = Downward acceleration
The velocities act the opposite ways, because they’re acting in opposite directions.
Downward velocity has a negative sign, indicating downward direction.
Inclined planes showed Galileo that the distance of a uniformly accelerating object is proportional to the square of time taken.
Distance travelled = 1/2 x acceleration x time x time
Shorthand notation: d = 1/2gt^2
d → distance object falls
t → time taken for the fall
Note:
→ For an object falling 5m during the first second of a 10m/s fall, it’d be expected to cover 10m. This can only actually happen if the average speed of the object is 10m/s for that entire second.
→ The average speed in this second is actually the sum of the starting and final speeds, divided by 2.
→ (0+10)/2, which is 5m/s.
Objects fall with unequal accelerations.
Eg: a leaf, a feather, and a sheet of paper fall at different speeds due to different air resistances.
This can be demonstrated with a closed glass tube containing these objects.
If the air in the tube is replaced with a vacuum, the objects will fall at the same speed.
Heavier objects aren’t appreciably affected by air resistance.
v = gt and d = 1/2 gt^2 tell us about objects falling in the air from an initial state of rest.
For an object falling, we are talking about speed or velocity.
v = gt
For how far an object falls, we are talking about distance.
d = 1/2 gt^2
Velocity is a rate (rate of change of position).
Acceleration is a rate of a rate (rate of change of velocity).
Athletes and dancers appear to “hang in the air” for 2 to 3 seconds when they jump.
This is actually one 1 second.
People can easily cross over a 0.5 m gate, but they wouldn’t be able to jump 0.5 m high.
It’s easier for people to leap over a fence than to shift their center of gravity entirely.
When you jump upwards, you only apply force when your feet are in contact with the ground. As soon as you’re in the air, your upward speed decreases at a rate of 10m/s^2. At the topmost point, your speed is 0.
When you start to fall, your speed increases at the same rate.
Hang rate is the sum of the rising time and the falling time.
Relationship between up or down and vertical height:
d = 1/2gt^2 , or,
t = square root of (2*d/g)
Speed → how fast
Velocity → how fast + in what direction
Speed is a scalar quantity. Velocity is a vector quantity.
Eg: Consider an airplane flying 80 km/h due north getting caught in a 60 km/h crosswind and getting thrown off course by it.
A crosswind is a wind blowing at a 90˚angle to the object being mentioned. Here, the plane.
If the 80 km/h vector is 4 cm long, and the 60 km/h vector is 3 cm, the resultant of the two vectors is a 100km/h vector measuring 5 cm long, at an angle of 37˚ from the 60 km/h vector.
The plane is due eastward.
All motion is relative.
If unstated, the motion mentioned is relative to the surface of the Earth.
Even things that are at rest are moving.
You’re moving at 170,000 km/h right now.
Before Galileo, people described things as either slow or fast.
Galileo was the first to measure speed.
Speed = Distance/Time
Galileo measured distance easily. He struggled with measuring time.
Sometimes he used his own pulse, or dripping water drops.
Eg: Cyclist covering 16 meters in 2 seconds has a speed of 8 meters per second (m/s).
Instantaneous speed is the speed of an object at any instant.
If a car travelled at 50 km/h for an hour, it would cover 50 km. If it travelled for half an hour, it would cover 25 km.
Average speed = total distance covered/time interval
Eg: if you travel 320 km in 4 hrs, the average speed is 80 km/h.
Average speed doesn’t tell you the different speeds at smaller time intervals.
Average speed is different from instantaneous speed.
Total distance covered = average speed x time interval
The speed and direction of motion for an object gives us its velocity.
Speed → car travelling at 60 km/h.
Velocity → car moving at 60 km/h towards north.
Speed is how fast an object moves.
Velocity is how fast an object moves and in what direction it moves.
Vector quantity: Quantity that specifies magnitude and direction.
Scalar quantity: Quantity that specifies only magnitude.
Constant speed is steady speed.
Constant velocity is constant speed and constant direction.
Constant direction means the object moves in a straight line. The path doesn’t curve.
Constant velocity → Motion in a straight line at a constant speed.
Velocity changes if speed or direction or both change.
Velocity of an object changes with a change in speed, change in direction, or change in both.
Acceleration → How quickly the velocity changes and in what direction.
Formula → Acceleration = change of velocity/time interval
Acceleration is defined by change.
Eg: increasing velocity from 30 km/h to 35 km/h in one second, to 40 km/h in the next, 45 km/h in the next, and so on.
Here, the acceleration is 5 km/h.s
Acceleration is the change per second in the velocity.
Acceleration is the increase or decrease in the velocity.
Deceleration → When there is a large decrease per second in the velocity.
When we move in a curved path, our direction is constantly changing, so we are accelerating, even if we are moving at a constant speed.
Eg: Standing in a moving bus. When a bus moves at a constant velocity, you can stand with no extra effort. When the bus accelerates, you experience difficulty standing.
Galileo demonstrated acceleration using experiments on inclined planes.
A ball rolling down an inclined plane picks up the same speed with each successive second. This is constant acceleration.
Eg: For a ball rolling down a plane inclined at an angle, let’s say it picks up a speed of 2 m/s with each second.
The instantaneous velocity at 1s intervals at this acceleration is 0, 2, 4, 6, 8, 10 m/s, and so on.
Velocity acquired = acceleration x time
At the end of 1s, the ball travels 2 m/s, at the end of 2s, it is travelling 4 m/s, at the end of 10s, it’s 20 m/s.
Acceleration down an incline is constant for each incline.
Steeper inclines have greater accelerations.
When the incline is tipped vertically, the ball accelerates to its highest extent. It falls with the acceleration of a falling object.
When air resistance can be ignored, all objects fall with the same acceleration.
When an object falls under the influence of only gravity, it is in a state of free fall.
There’s no other restraints like friction with the air acting on the object.
Instantaneous velocity of a free falling object at 1 second intervals:
Time of Fall (s) | Velocity Acquired (m/s) |
|---|---|
0 | 0 |
1 | 10 |
2 | 20 |
3 | 30 |
4 | 40 |
5 | 50 |
t | 10t |
During each second, the object gains a speed of 10 m/s.
Gain per second is the acceleration.
Free fall acceleration = 10 m/s^2.
For free falling objects, g represents acceleration.
Acceleration is due to gravity.
g is slightly different on the surface of the Moon and the surfaces of other planets.
Average value of g = 9.8 m/s2
Instantaneous velocity, v = gt
Speedometers can be used to measure free fall acceleration.
For an object thrown upwards:
It slows down as it moves upwards.
At its highest point, it changes direction.
At its highest point, its instantaneous speed becomes 0.
When it starts moving downwards, it acts like its been dropped from rest at that height.
Upward deceleration = Downward acceleration
The velocities act the opposite ways, because they’re acting in opposite directions.
Downward velocity has a negative sign, indicating downward direction.
Inclined planes showed Galileo that the distance of a uniformly accelerating object is proportional to the square of time taken.
Distance travelled = 1/2 x acceleration x time x time
Shorthand notation: d = 1/2gt^2
d → distance object falls
t → time taken for the fall
Note:
→ For an object falling 5m during the first second of a 10m/s fall, it’d be expected to cover 10m. This can only actually happen if the average speed of the object is 10m/s for that entire second.
→ The average speed in this second is actually the sum of the starting and final speeds, divided by 2.
→ (0+10)/2, which is 5m/s.
Objects fall with unequal accelerations.
Eg: a leaf, a feather, and a sheet of paper fall at different speeds due to different air resistances.
This can be demonstrated with a closed glass tube containing these objects.
If the air in the tube is replaced with a vacuum, the objects will fall at the same speed.
Heavier objects aren’t appreciably affected by air resistance.
v = gt and d = 1/2 gt^2 tell us about objects falling in the air from an initial state of rest.
For an object falling, we are talking about speed or velocity.
v = gt
For how far an object falls, we are talking about distance.
d = 1/2 gt^2
Velocity is a rate (rate of change of position).
Acceleration is a rate of a rate (rate of change of velocity).
Athletes and dancers appear to “hang in the air” for 2 to 3 seconds when they jump.
This is actually one 1 second.
People can easily cross over a 0.5 m gate, but they wouldn’t be able to jump 0.5 m high.
It’s easier for people to leap over a fence than to shift their center of gravity entirely.
When you jump upwards, you only apply force when your feet are in contact with the ground. As soon as you’re in the air, your upward speed decreases at a rate of 10m/s^2. At the topmost point, your speed is 0.
When you start to fall, your speed increases at the same rate.
Hang rate is the sum of the rising time and the falling time.
Relationship between up or down and vertical height:
d = 1/2gt^2 , or,
t = square root of (2*d/g)
Speed → how fast
Velocity → how fast + in what direction
Speed is a scalar quantity. Velocity is a vector quantity.
Eg: Consider an airplane flying 80 km/h due north getting caught in a 60 km/h crosswind and getting thrown off course by it.
A crosswind is a wind blowing at a 90˚angle to the object being mentioned. Here, the plane.
If the 80 km/h vector is 4 cm long, and the 60 km/h vector is 3 cm, the resultant of the two vectors is a 100km/h vector measuring 5 cm long, at an angle of 37˚ from the 60 km/h vector.
The plane is due eastward.
