1 D Kinematics Particle Under Constant Acceleration Average
![1 -D Kinematics Particle Under Constant Acceleration 1 -D Kinematics Particle Under Constant Acceleration](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-1.jpg)
![Average Acceleration l Acceleration is the rate of change of the velocity: l SI Average Acceleration l Acceleration is the rate of change of the velocity: l SI](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-2.jpg)
![Instantaneous Acceleration l The instantaneous acceleration is the limit of the average acceleration as Instantaneous Acceleration l The instantaneous acceleration is the limit of the average acceleration as](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-3.jpg)
![Acceleration: velocity – time graph l The slope on the velocitytime graph reveals the Acceleration: velocity – time graph l The slope on the velocitytime graph reveals the](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-4.jpg)
![Acceleration: position – time graph l Graph curves towards time axis = particle slows Acceleration: position – time graph l Graph curves towards time axis = particle slows](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-5.jpg)
![Acceleration and Velocity l When an object’s velocity and acceleration are in the same Acceleration and Velocity l When an object’s velocity and acceleration are in the same](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-6.jpg)
![Acceleration and Velocity l l Images are equally spaced. The car is moving with Acceleration and Velocity l l Images are equally spaced. The car is moving with](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-7.jpg)
![Acceleration and Velocity l l Velocity and acceleration are in the same direction Acceleration Acceleration and Velocity l l Velocity and acceleration are in the same direction Acceleration](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-8.jpg)
![Acceleration and Velocity l l Acceleration and velocity are in opposite directions Acceleration is Acceleration and Velocity l l Acceleration and velocity are in opposite directions Acceleration is](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-9.jpg)
![Acceleration and Velocity l In all the previous cases, the acceleration was constant l Acceleration and Velocity l In all the previous cases, the acceleration was constant l](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-10.jpg)
![Kinematic Equations – The Big Four Kinematic Equations – The Big Four](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-11.jpg)
![Kinematic Equations l The kinematic equations can be used with any particle under uniform Kinematic Equations l The kinematic equations can be used with any particle under uniform](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-12.jpg)
![Kinematic Equations l For constant acceleration: l Can determine an object’s velocity at any Kinematic Equations l For constant acceleration: l Can determine an object’s velocity at any](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-13.jpg)
![Kinematic Equations, specific l For constant acceleration: l The average velocity can be expressed Kinematic Equations, specific l For constant acceleration: l The average velocity can be expressed](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-14.jpg)
![Kinematic Equations, specific l For constant acceleration: l This gives you the position of Kinematic Equations, specific l For constant acceleration: l This gives you the position of](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-15.jpg)
![Kinematic Equations, specific l For constant acceleration: l Gives final position in terms of Kinematic Equations, specific l For constant acceleration: l Gives final position in terms of](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-16.jpg)
![Kinematic Equations, specific l For constant acceleration: l Gives final velocity in terms of Kinematic Equations, specific l For constant acceleration: l Gives final velocity in terms of](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-17.jpg)
![When a = 0 l When the acceleration is zero, l l l vxf When a = 0 l When the acceleration is zero, l l l vxf](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-18.jpg)
![Example l A train starts from rest and moves with constant acceleration. It reaches Example l A train starts from rest and moves with constant acceleration. It reaches](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-19.jpg)
- Slides: 19
![1 D Kinematics Particle Under Constant Acceleration 1 -D Kinematics Particle Under Constant Acceleration](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-1.jpg)
1 -D Kinematics Particle Under Constant Acceleration
![Average Acceleration l Acceleration is the rate of change of the velocity l SI Average Acceleration l Acceleration is the rate of change of the velocity: l SI](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-2.jpg)
Average Acceleration l Acceleration is the rate of change of the velocity: l SI units are m/s² In one dimension, positive and negative can be used to indicate direction. l
![Instantaneous Acceleration l The instantaneous acceleration is the limit of the average acceleration as Instantaneous Acceleration l The instantaneous acceleration is the limit of the average acceleration as](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-3.jpg)
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 velocity time graph l The slope on the velocitytime graph reveals the Acceleration: velocity – time graph l The slope on the velocitytime graph reveals the](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-4.jpg)
Acceleration: velocity – time graph l The slope on the velocitytime graph reveals the acceleration: l l l Slope of the green (tangent) line represents the instantaneous acceleration. Slope of the blue (secant) line is the average acceleration. Constant acceleration: graph is linear, average and instantaneous values are equal The area under the graph corresponds to the displacement of the particle
![Acceleration position time graph l Graph curves towards time axis particle slows Acceleration: position – time graph l Graph curves towards time axis = particle slows](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-5.jpg)
Acceleration: position – time graph l Graph curves towards time axis = particle slows down l Graph curves away from time axis = particle slows down Graph is linear = particle moves at constant velocity, so acceleration is zero. l
![Acceleration and Velocity l When an objects velocity and acceleration are in the same Acceleration and Velocity l When an object’s velocity and acceleration are in the same](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-6.jpg)
Acceleration and Velocity l When an object’s velocity and acceleration are in the same direction, the object is speeding up. l When an object’s velocity and acceleration are in opposite directions, the object is slowing down. l If possible, take initial velocity direction as positive. If not, don’t.
![Acceleration and Velocity l l Images are equally spaced The car is moving with Acceleration and Velocity l l Images are equally spaced. The car is moving with](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-7.jpg)
Acceleration and Velocity l l Images are equally spaced. The car is moving with constant positive velocity (shown by red arrows maintaining the same size) Acceleration equals zero
![Acceleration and Velocity l l Velocity and acceleration are in the same direction Acceleration Acceleration and Velocity l l Velocity and acceleration are in the same direction Acceleration](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-8.jpg)
Acceleration and Velocity l l Velocity and acceleration are in the same direction Acceleration is uniform (violet arrows, same length) Velocity is increasing (red arrows are getting longer) This shows positive acceleration and positive velocity
![Acceleration and Velocity l l Acceleration and velocity are in opposite directions Acceleration is Acceleration and Velocity l l Acceleration and velocity are in opposite directions Acceleration is](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-9.jpg)
Acceleration and Velocity l l Acceleration and velocity are in opposite directions Acceleration is uniform Velocity is decreasing (red arrows are getting shorter) Positive velocity and negative acceleration
![Acceleration and Velocity l In all the previous cases the acceleration was constant l Acceleration and Velocity l In all the previous cases, the acceleration was constant l](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-10.jpg)
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.
![Kinematic Equations The Big Four Kinematic Equations – The Big Four](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-11.jpg)
Kinematic Equations – The Big Four
![Kinematic Equations l The kinematic equations can be used with any particle under uniform Kinematic Equations l The kinematic equations can be used with any particle under uniform](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-12.jpg)
Kinematic Equations l The kinematic equations can be used with any particle under uniform acceleration. l You may need to use two (or more) of the equations to solve one problem. l l x, v, a can be either positive or negative! Many times there is more than one correct way to solve a problem.
![Kinematic Equations l For constant acceleration l Can determine an objects velocity at any Kinematic Equations l For constant acceleration: l Can determine an object’s velocity at any](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-13.jpg)
Kinematic Equations l For constant acceleration: l Can determine an object’s velocity at any time t when we know its initial velocity and its acceleration. l l Assumes ti = 0 and tf = t Does not give any information about displacement.
![Kinematic Equations specific l For constant acceleration l The average velocity can be expressed Kinematic Equations, specific l For constant acceleration: l The average velocity can be expressed](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-14.jpg)
Kinematic Equations, specific l For constant acceleration: l The average velocity can be expressed as the arithmetic mean of the initial and final velocities.
![Kinematic Equations specific l For constant acceleration l This gives you the position of Kinematic Equations, specific l For constant acceleration: l This gives you the position of](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-15.jpg)
Kinematic Equations, specific l For constant acceleration: l This gives you the position of the particle in terms of time and velocities. l Doesn’t give you the acceleration.
![Kinematic Equations specific l For constant acceleration l Gives final position in terms of Kinematic Equations, specific l For constant acceleration: l Gives final position in terms of](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-16.jpg)
Kinematic Equations, specific l For constant acceleration: l Gives final position in terms of velocity and acceleration. l Doesn’t tell you about final velocity.
![Kinematic Equations specific l For constant acceleration l Gives final velocity in terms of Kinematic Equations, specific l For constant acceleration: l Gives final velocity in terms of](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-17.jpg)
Kinematic Equations, specific l For constant acceleration: l Gives final velocity in terms of acceleration and displacement. l Does not give any information about the time.
![When a 0 l When the acceleration is zero l l l vxf When a = 0 l When the acceleration is zero, l l l vxf](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-18.jpg)
When a = 0 l When the acceleration is zero, l l l vxf = vxi = vx xf = xi + vx t i. e. , constant acceleration includes constant velocity as a special case.
![Example l A train starts from rest and moves with constant acceleration It reaches Example l A train starts from rest and moves with constant acceleration. It reaches](https://slidetodoc.com/presentation_image/19654fc91e82b3cf9144e9c4ffe96352/image-19.jpg)
Example l A train starts from rest and moves with constant acceleration. It reaches 30 m/s the moment it has traveled 150 m. Calculate: l The acceleration of the train, and the time it takes to travel the first 150 m; l The time it takes, and the distance it travels between reaching 30 m/s until it reaches 50 m/s.
Particle under constant acceleration
Aplusphysics kinematics-horizontal kinematics
Kinematics of a particle
Kinematics of a particle
Kinematics of a particle
Kinematics of a particle
Constant acceleration equations
4 kinematic equations
Kinematics of rigid body
Kinetics of a particle: force and acceleration
Radial acceleration definition
Kinetic angular energy
Centripetal acceleration ac
Centripetal acceleration tangential acceleration
Relationship between linear and angular quantities
Average acceleration
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Average acceleration
What does constant acceleration mean
Non constant acceleration