Kinematics Of Rectilinear Motion k5o48

DYNAMICS – Is that branch of Mechanics that consider the study of the effect of forces to bodies that are in motion.

KINEMATICS OF RECTILINEAR MOTION

Two Major Divisions/ Branches of Dynamics:

Engr. Jerome Famadico

11/12/2015

1. KINEMATICS – defines the motion of a particle or body without consideration of the forces causing the motion.

2. KINETICS – relates the force acting on a body to its mass and acceleration Prepared by: Engr. Jerome Jordan F. Famadico, CE

The term “body” denotes a system of particles which form an object of appreciable size.

- Is the time rate of change of displacement -Velocity is considered positive when the displacement X is increasing with time t and negative when it is decreasing with time t.

-Displacement is positive (+) when to the right of the origin O and negative (-) when to the left.

Engr. Jerome Famadico

Velocity (ν) (m/sec) :

-The displacement of a particle is the vector distance travelled from an origin to the position occupied by a particle on its path.

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The term “particle” usually denotes an object at point size.

Displacement (S) (meter) :

Acceleration (a) (m/sec2) : -Acceleration is positive when accelerating and negative when decelerating.

Engr. Jerome Famadico

Difference between Particles and Bodies:

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Instructor

-In case of “free-falling-bodies”, “a” is replaced by “g” which is constant (9.81 m/sec2) -If the motion is non-uniform, its velocity is changing with time and therefore we have acceleration.

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1.

V = Vo + at

2.

s = Vot + (½) at2

3.

V2 = Vo2 + 2as

Standard Signs: 1. The initial direction of motion represents the positive direction for displacement, velocity, and acceleration. 2. Negative value obtained in applying the equation would mean that velocity is directly opposite to the initial direction of motion. 3. Negative value of displacement would indicate that the position of the moving particle is to be measured back from the origin of displacement. 4. If the particle is moving along a straight line and return to its starting position, displacement will be zero.

SAMPLE PROBLEMS: 1. The car in the Figure below moves in a straight line such that for a short time its velocity is defined by v = (3t2 + 2t) ft/sec, where t is in seconds. Determine its position and acceleration when t = 3 s. When t = 0, s = 0.

V Vo a t s

= final velocity (m/s) = initial velocity (m/s) = acceleration (m/s2) = time (sec) = displacement (m)

KINEMATICS OF RECTILINEAR MOTION: Tabulation of Formulas: Required t=? a=?

Given A, Vo, V t; Vo; V t; Vo; s Vo; V; s

Formula t = (V – Vo)/a a = (V – Vo)/t a = (2s – 2Vot)/t2 a = (V2 – Vo2)/2s

Vo = ?

t; a; V t; a; s a; V; s

Vo = (V – at) Vo = (s/t) – (at/2) Vo =

V=?

t; a; Vo a; Vo; s

s=?

t; a; Vo a; Vo; V t; Vo; V

V2 - 2as

V = Vo + at V=

Engr. Jerome Famadico

KINEMATICS OF RECTILINEAR MOTION:

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Where:

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The Three Kinematic Equations:

Engr. Jerome Famadico

Translation – motion on which a straight line es through any two particles on a body which is always parallel to its position. If the path is straight, the motion is called rectilinear motion. If the path is curved, the motion is called curvilinear motion.

KINEMATICS OF RECTILINEAR MOTION:

V2 + 2as

s = Vot + ½ (at2) s = (V2 – Vo2)/2a s = ½ (t) (Vo + V)

SAMPLE PROBLEMS: 2. A car starts from rest and travels on a straight road with a constant acceleration of 6 m/sec2 for 4 seconds. After which it maintains a constant speed for 2 seconds. Finally, it decelerates at 8 m/sec2 until it stops. Determine the total distance and average speed of the car.

Engr. Jerome Famadico

RECTILINEAR TRANSLATION :

Engr. Jerome Famadico

11/12/2015

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SAMPLE PROBLEMS: 5. A stone is thrown upward from the ground with a constant velocity of 15 m/sec. One second later another stone is thrown vertically upward with a velocity of 30 m/sec. How far above the ground will the stones be at the same level?

SAMPLE PROBLEMS:

4. A car was travelling at a speed of 50 mph. The driver saw a road block 80 m ahead and stepped on the brake causing the car to decelerate uniformly at 10 m/s2. Find the distance from the roadblock to the point where the car stopped. Assume perception reaction time is 2 seconds.

6. A ball is thrown vertically upward with an initial velocity of 3 m/sec from the window of a tall building. The ball strikes the sidewalk at the ground level 4 seconds later. Determine the velocity with which the ball hits the ground.

Engr. Jerome Famadico

SAMPLE PROBLEMS:

Engr. Jerome Famadico

3. Cars A & B approach each other on a straight road 450 meters apart. Car A has an initial velocity of 45 MPH and is decelerating at a rate of 1.4 m/sec2. Car B has an initial velocity of 12 MPH and is accelerating at a rate of 1 m/sec2. When will the two cars meet and how far will each car travel?

Engr. Jerome Famadico

SAMPLE PROBLEMS:

Engr. Jerome Famadico

11/12/2015

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