Lecture 2 Physics 107

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Lecture 2 PHY 107)SPRING 2016

INSTRUCTOR : SUBIR GHOSH, PHD

http://www.northsouth.edu/index.html


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Kinematics

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Kinematics deals with the motion of objects.

Motions can be divided into three types:

Translational

: Car moving down the highway

Rotational

: Earth’ spin on its axis

Vibrational

: Back and forth motion of a pendulum

In translational motion, moving objects are considered as particles regardless of their sizes. A particle ipoint-like mass having infinitesimal size.


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Displacement

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The displacement of a particle is defined as the change in position.

∆x = − 1

Displacement is an example of a vector quantity. It is positive if the particle has moved in the positivedirection of the x-axis and negative if the particle has moved in the negative direction of the x-axis.

A vector is a physical quantity that requires the specification of both direction and magnitude. Bycontrast a scalar is a quantity that has magnitude but no direction.

Features of Displacement:

1. Its magnitude is the distance between the original and the final position2. Its direction can be represented by a plus sign or a minus sign if the motion is along a single axis


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Average Velocity

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The average velocity of a particle is defined as the particle’s displacement divided by the time interval durinwhich the displacement occurred.

=∆∆

= − 1 − 1


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Average Speed

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The average speed of a particle, a scalar quantity, is defined as the total distance traveled divided by thetotal time it takes to travel that distance:

= ∆

Average speed does not include direction. Sometimes, average velocity is the same as average speed.However, for some cases the two could be quite different.


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Sample Problem Page 16)

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You drive a pick up truck along a straight road for 8.4km at 70km/hr, at which point the truck runs outgasoline and stops. Over the next 30 minutes, you walk another 2.0km farther along the road togasoline station.

a. What is your overall displacement from the beginning of your drive to the arrival at your station?b. What is the time interval from the beginning of your drive to your arrival at the station?


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Sample Problem Page 16) contd.

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c. What is the average velocity from the beginning of your drive to your arrival at the station?

d. Suppose that to pump the gasoline, pay for it and walk back to the truck takes you another 45 minutWhat is your average speed from the beginning of your drive to your return to the truck with thegasoline?


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Instantaneous Velocity

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Instantaneous velocity is defined as the velocity of a particle at a given instant.

The velocity at a given instant is obtained from the average velocity by the shrinking the time intervalcloser and closer to zero. As Δ t dwindles, the average velocity approaching a limiting value, which velocity at that instant:

= lim∆ →

∆

∆

=

Speed is the magnitude of velocity, for example, a velocity of 5m/sec and one of -5m/sec both have anassociated speed of 5m/sec


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Acceleration

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The average acceleration of a particle is defined as the change in velocity Δv x divided by the tiduring which that change has occurred

= ∆

∆

The instantaneous acceleration (simply acceleration) is =

=

• The acceleration of a particle is the second derivative of its position with respect to time.

• It is a vector quantity, having both magnitude and direction .


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Sample Problem Page 21)

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A particle’s position on the x -axis is given by = 4 − 27 + 3 with x in meters and t is secon

a. Find the particle’s velocity function v(t) and acceleration function a(t).b. Is there a time when = 0 ?


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Exercise

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The velocity of a particle moving along the x-axis varies in time according to the expression


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Constant Acceleration

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Note that there is a subtle difference betwe2-15 and 2-18 – one involves the initial vother involves the velocity v at time t .


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Constant Acceleration

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Which one of the following equations represents constant acceleration ?

a. = −5 3 + 4 + 6b. = 5 - 3


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Freely Falling Object

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• A freely falling object is any object moving freely under the influence of gravity alone, regardlessinitial motion

• Objects thrown upward or downward and those released from rest are all freely falling once they areleased.

• Any freely falling object experiences an acceleration directed downward , regardlessmotion.

• The free-fall acceleration is negative – that is , downward on the y-axis, toward Earth’s cen

• It has a value – g in the equations, - g = -9.8m/s 2 . The magnitude of acceleration is g = 9.8


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Example

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A ball is tossed straight up at 25m/sec. Estimate its velocity every 1sec.


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Sample Problem

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A pitcher tosses a baseball up along a y-axis with an initial speed of 12m/sec.

a. How long does the ball take to reach its maximum height?b. What is the ball’s maximum height above the release point?c. How long does the ball take to reach a point 5.0m above its release point?

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Lecture 2 Physics 107