Linear Motion

Motion Is Relative

Motion is always described relative to a reference point. For example, when you walk on the road, your movement is relative to the Earth, but the Earth itself is moving relative to the Sun. Thus, your motion relative to the Sun differs from your motion relative to the Earth.

• Reference Frame: The perspective from which motion is measured.

• Example: A passenger walking inside a moving train is moving relative to the train and also relative to the ground outside.

Speed

Speed is defined as the distance covered per unit of time. It is a scalar quantity, meaning it has magnitude but no direction.

• Formula:

• Units: Meters per second (m/s) in SI units.

• Example: If a girl runs 4 meters in 2 seconds, her speed is .

Average Speed

Average speed is the total distance traveled divided by the total time taken. It does not account for variations in speed during the journey.

• Formula:

• Example: Driving 200 km in 2 hours yields an average speed of .

Instantaneous Speed

Instantaneous speed is the speed of an object at a specific moment in time. It is what is shown on a speedometer.

• Definition: The rate at which distance is covered at a particular instant.

• Example: A car's speedometer shows the instantaneous speed, which may differ from the average speed over a trip.

Velocity

Velocity is a vector quantity that describes both the speed and direction of an object's motion. It is often referred to as "directed speed."

• Formula:

• Magnitude: The speed component.

• Direction: The direction of motion.

• Example: A car moving east at 60 km/h has a velocity of 60 km/h east.

Speed vs. Velocity

While speed is the rate of motion regardless of direction, velocity includes direction. Constant speed means steady speed, while constant velocity means both steady speed and unchanging direction.

• Constant Speed: No change in magnitude.

• Constant Velocity: No change in magnitude or direction (straight-line motion).

Acceleration

Acceleration is the rate at which velocity changes over time. It can involve changes in speed, direction, or both.

• Formula:

• Units: Meters per second squared (m/s2).

• Example: If a car's speed increases from 40 km/h to 45 km/h in 5 seconds, the acceleration is .

• Change in Direction: Turning at constant speed is still acceleration.

Free Fall

Free fall refers to motion under the influence of gravity only, with no air resistance. All objects in free fall near Earth's surface accelerate at approximately 9.8 m/s2 (often rounded to 10 m/s2 for simplicity).

• Velocity after time t:

• Distance after time t:

• Example: After 1 second, a dropped object has a speed of 10 m/s; after 2 seconds, 20 m/s, and so on.

Velocity Vectors

Velocity vectors combine magnitude and direction. When two velocities are combined (such as wind and airplane speed), the resultant velocity is found using vector addition, often visualized with the parallelogram rule.

• Resultant Velocity: The vector sum of two or more velocities.

• Example: An airplane flying with a crosswind combines its velocity with the wind's velocity to determine its actual path and speed.

Summary Table: Speed, Velocity, and Acceleration

Example Problems

• Average Speed: Driving 60 km in 2 hours yields an average speed of .

• Free Fall Distance: After 4 seconds, a freely falling object covers meters.

• Vector Addition: An airplane flying at 80 km/h with a 60 km/h crosswind has a resultant speed of 100 km/h; with an 80 km/h crosswind, the resultant is 113 km/h at a 45-degree angle.

Additional info:

• For inclined planes, Galileo found that steeper inclines produce greater accelerations, with maximum acceleration occurring in vertical free fall.

• Acceleration can occur even if speed is constant, as long as direction changes (e.g., turning a corner).