Lecture No.1

Bahauddin Zakariya University

Multan

Mechanical Engineering

Engineering Mechanics-II (Dynamics)

BY

Engr. Abdul Bari

Lecture 1:

Objective

To introduce the concepts of position, displacement, velocity, and acceleration.

To study particle motion along a straight line.

Rectilinear Kinematics
Section 12.2

Rectilinear :   Straight line motion

Kinematics :   Study the geometry of the motion dealing with   s, v, a, & t.

Rectilinear Kinematics : To identify at any given instant, the particle’s position, velocity, and acceleration.

(All objects such as rockets, projectiles, or vehicles will be considered as particles “has negligible size and shape”

particles : has mass but  negligible size and shape

Position

Position : Location of a particle at any given instant with respect to the origin

r : Displacement ( Vector )

s : Distance ( Scalar )

Displacement

Displacement : defined as the change in position.

 r : Displacement  ( 3 km )

 s : Distance         ( 8 km )

    Total length

Vector is direction oriented

D s   positive

D s  negative

Velocity & Speed

Velocity : Displacement per unit time

Average velocity :

            V = Dr  / Dt

Speed : Distance per unit time

Average speed :

  usp = sT / Dt (Always positive scalar )

Speed refers to the magnitude of velocity

Average velocity :

 uavg = Ds / Dt

Velocity (con.)

Instantaneous velocity :

For straight-line       Dr = Ds

Acceleration

Acceleration : The rate of change in velocity

Average acceleration :

Instantaneous acceleration :

If v ‘ > v     “ Acceleration “

If v ‘ < v      “ Deceleration”

Relation involving s, v, and s
No time t

Position   s

Velocity 

Acceleration

Problem 12.18

A car starts from rest and moves along a straight line with an acceleration of a = ( 3 s -1/3 ) m/s2. where s is in meters. Determine the car’s acceleration when t = 4 s.

Rest  t = 0 , v = 0

For constant acceleration
a = ac

Velocity as a Function of Time

Position as a Function of Time

velocity as a Function of Position

Summary

Time dependent acceleration

Constant acceleration

Example 12.1

Example 12.2

Example 12.3

Example 12.4

Example 12.5

Problem # 12.5