Chapter 2 Particle Under Constant Acceleration Average Acceleration

Chapter 2 Particle Under Constant Acceleration

Average Acceleration l Acceleration is the rate of change of the velocity l Dimensions are L/T 2. SI units are m/s². In one dimension, positive and negative can be used to indicate direction. l l

Instantaneous Acceleration l The instantaneous acceleration is the limit of the average acceleration as t approaches 0 l The term acceleration will mean instantaneous acceleration l If average acceleration is wanted, the word average will be included

Acceleration and Velocity l When an object’s velocity and acceleration are in the same direction, the object is speeding up (speed increases). l When an object’s velocity and acceleration are in the opposite directions, the object is slowing down (speed decreases). l If possible, take initial velocity direction as positive. If not, don’t.

Acceleration and Velocity l l Images are equally spaced. Speed Velocity Acceleration

Acceleration and Velocity l l l Spacing btw images increases. Speed Velocity Acceleration Velocity and acceleration

Acceleration and Velocity l l l Spacing btw images decreases. Speed Velocity Acceleration Velocity and acceleration

Acceleration – time graph l The zero slope indicates a constant acceleration

Velocity – time graph l l The slope of the velocity-time graph is the acceleration: l Slope of the green (tangent) line represents the instantaneous acceleration at the moment tf. l Slope of the blue (secant) line is the average acceleration between ti and tf. The area between the graph and the time axis represents the displacement.

Velocity – time graph l The slope gives the acceleration l The straight line indicates a constant acceleration

Position - time graph l l l Position: read directly from the graph Velocity: measure the slope Acceleration: check the curvature

Acceleration and Velocity l In all the previous cases, the acceleration was constant l l Shown by the violet arrows all maintaining the same length The diagrams represent motion of a particle under constant acceleration.

Graphical Look at Motion: displacement – time curve l l The slope of the curve is the velocity The curved line indicates the velocity is changing (increasing) l Therefore, there is an acceleration (parallel to velocity)

Graphical Motion with Constant Acceleration l A change in the acceleration affects the velocity and position l Note especially the graphs when a = 0

Test Graphical Interpretations l Match a given velocity graph with the corresponding acceleration graph.