Kinematics

Prepared By:Abdul Rafae (13-EE(P)-003)Ali Hamza (13-EE(P)-009)KinematicsOrigin of kinematicsBranch of mechanicsWhat is mechanics?Mechanics is the branch of physics that focuses on the motion of objects and the forces that cause the motion to change.

There are two parts to mechanics: Kinematics and Dynamics

DefinitionKinematics often deals with the concepts that are needed to describe motion, without any reference to forces.For Example:DistanceDisplacementVelocityAccelerationKinematics..???Kinematic is further divided in smaller categories according to the motion of particle under supervision:Continuous MotionCurvilinear MotionProjectile motionTypes of KinematicsThe continuous motion of a particle whose mass, shape and size is negligible at any instant of time t is specified by:PositionDisplacementDistanceSpeedVelocityAccelerationContinuous MotionPosition (x) where you are locatedThe straight-line path of a particle using a single coordinate axis is called position. The origin 0 on the path is a fixed point, and from this point the position coordinate s is used to specify the location of the particle at any given instant.

Position of particle

Displacement (x) where you are in relation to where you startedDisplacement is also the shortest distance from starting point to the ending point.Displacement

Distance (d ) how far you have traveled from the starting point, regardless of direction

DistanceYou drive the path, and your odometer goes up by 8 miles (your distance).Your displacement is the shorter directed distance from start to stop (green arrow).Question: What if you drove in a circle?Distance vs. DisplacementstartstopSpeed

VelocitySpeed is a scalar (how fast something is moving regardless of its direction). Example: v = 20 mphSpeed is the magnitude of velocity.Velocity is a combination of speed and direction. Ex: v = 20 mph at 15 south of westThe symbol for speed is v.The symbol for velocity is type written in bold: v or hand written with an arrow: v

Speed vs. VelocityAcceleration Acceleration how fast you speed up, slow down, or change direction; its the rate at which velocity changes. Two examples:Accelerationt (s) v (mph)055157259361t (s) v (m/s)034131228325a = +2 mph / sa = -3m / ss = -3 m / s 2Velocity & Acceleration Sign ChartV E L O C I T Y ACCELERATION+-+Moving forward;Speeding upMoving backward;Slowing down -Moving forward;Slowing downMoving backward;Speeding upAcceleration due to Gravity

a = -g = -9.8 m/s2 9.8 m/s2Near the surface of the Earth, all objects accelerate at the same rate (ignoring air resistance)..This acceleration vector is the same on the way up, at the top, and on the way down!Formulas (derivations to follow)vf = v0 + a t vavg = (v0 + vf ) / 2x = v0 t + a t 2vf2 v02 = 2 a x

For 1-D motion with constant acceleration:A car starts from rest and with constant acceleration achieves a velocity of 15 m/s when it travels a distance of 200 m. Determine the acceleration of the car and the time required.Examples

Curvilinear motion occurs when a particle moves along a curved path.

Curvilinear Motion

DisplacementVelocity

Velocity

Acceleration

Curvilinear Motion: RectangularComponents

Examples

The truck travels along a circular road that has a radius of 50 m at a speed of 4 m/s. For a short distance when t = 0, its speed is then increased by a, = (0.4t) m/s2, where t is in seconds. Determine the speed and the magnitude of the truck's acceleration when t = 4 s.

Projectile Motion

Example