Mechanics: Motion

Mechanics: Motion

Definition of Motion in Mechanics

• Motion is a change in position of an object with respect to its surroundings in a given period of time.
• Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and time.

Mathematical Formulas

• The formula for velocity (v) is v = ∆x / ∆t, where ∆x is displacement and ∆t is total time taken.
• The formula for acceleration (a) is a = ∆v / ∆t, where ∆v is change in velocity and ∆t is total time taken.
• The formula for speed (s) in terms of distance (d) and time (t) is s = d / t. Speed is a scalar quantity while velocity is a vector.

Types of Motion

• Uniform motion is when an object moves with a constant speed or velocity.
• Non-uniform motion is when an object moves with a variable speed or velocity.
• Rectilinear motion refers to motion along a straight line.
• Circular motion refers to movement along the circumference of a circle.

Concepts of Motion in Mechanics

• Displacement: It is defined as the shortest distance between initial and final point in any direction. It is a vector quantity.
• Velocity: It is defined as the rate of change of displacement with time. It is a vector quantity.
• Acceleration: It is defined as the rate of change of velocity with time. It is a vector quantity.

Motion Graphs

• Distance-time graph: A straight line represents uniform motion, a horizontal line represents stationary object and non-linear line represents non-uniform motion.
• Velocity-time graph: A straight line indicates uniform acceleration, while a horizontal line denotes constant velocity. Area under the graph gives distance covered.

Importance of Units

• Pay close attention to the units in your calculations. Time is generally in seconds (s), distance in meters (m), speed and velocity in meters per second (m/s), and acceleration in meters per second squared (m/s²).
• When analysing or sketching motion graphs, do not forget to label axes with the correct quantities and units.