Linear Motion - Motion in One Dimension | Physics for JAMB PDF Download

Definition of Speed, Velocity, and Acceleration

1. Speed: Speed is a scalar quantity that measures how quickly an object covers a particular distance. It is the magnitude of velocity without considering direction. The formula for speed is given by:
Speed = Distance / Time
Example: A car travels 200 km in 4 hours. The speed of the car is 50 km/h.

2. Velocity: Velocity is a vector quantity that measures the rate of change of displacement with respect to time. It includes both magnitude and direction. The formula for velocity is given by:
Velocity = Displacement / Time
Example: A person walks 100 meters east in 20 seconds. The velocity of the person is 5 m/s east.

3. Acceleration: Acceleration is a vector quantity that measures the rate of change of velocity with respect to time. It indicates how quickly an object's velocity is changing. The formula for acceleration is given by:
Acceleration = Change in Velocity / Time
Example: A car increases its velocity from 20 m/s to 40 m/s in 5 seconds. The acceleration of the car is 4 m/s².

Equations of Uniformly Accelerated Motion

For an object moving with uniform acceleration, the following equations relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t):
v = u + at
s = ut + (1/2)at²
v² = u² + 2as

Motion Under Gravity

When an object is freely falling under the influence of gravity, it experiences constant acceleration called the acceleration due to gravity (g ≈ 9.8 m/s²). The equations for motion under gravity near the Earth's surface are:
v = u + gt
s = ut + (1/2)gt²

Distance-Time Graph and Velocity-Time Graph

• Distance-Time Graph: A distance-time graph represents how the distance traveled by an object changes with respect to time. The slope of the graph gives the object's speed.
  Example: A straight diagonal line on the graph indicates uniform speed.
• Velocity-Time Graph: A velocity-time graph represents how the velocity of an object changes with respect to time. The area under the graph gives the displacement of the object.
  Example: A horizontal line on the graph indicates constant velocity.

Instantaneous Velocity and Acceleration

• Instantaneous Velocity: Instantaneous velocity is the velocity of an object at a specific instant in time. It can be found by calculating the derivative of the displacement-time graph.
  Example: A car's instantaneous velocity at t = 5 seconds is 30 m/s.
• Instantaneous Acceleration: Instantaneous acceleration is the acceleration of an object at a specific instant in time. It can be found by calculating the derivative of the velocity-time graph.
  Example: A particle's instantaneous acceleration at t = 2 seconds is 10 m/s^2.

Key Concepts to Remember

• Speed is a scalar, velocity is a vector, and acceleration is a vector.
• Uniformly accelerated motion equations can be derived from basic kinematic principles.
• Motion under gravity near the Earth's surface experiences constant acceleration.
• Distance-time graphs show the change in distance with respect to time, and velocity-time graphs show the change in velocity with respect to time.
• Instantaneous velocity is the velocity at a specific instant, while instantaneous acceleration is the acceleration at a specific instant.

Candidates should focus on understanding the definitions, equations, and concepts mentioned above to successfully differentiate between speed, velocity, and acceleration, derive equations of uniformly accelerated motion, solve problems related to motion under gravity, interpret distance-time graphs and velocity-time graphs, and compute instantaneous velocity and acceleration.