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Acceleration1D motion with Constant AccelerationFree Fall

Lecture 04(Chap. 2, Sec. 6-10 )General Physics (PHYS101)Sections 30 and 33 are canceled and became section 27

Lightning ReviewDisplacement - change of position

Average velocity - displacement over time interval

Instantaneous velocity - the same but for very small time intervalLast lecture:

Average AccelerationAverage acceleration is the rate of change of the velocity Changing velocity (non-uniform) means an acceleration is presentAverage acceleration is a vector quantity (i.e described by both magnitude and direction)SI unit: m/s2

Instantaneous AccelerationInstantaneous acceleration is the limiting case of the average acceleration as the time interval goes to zero.Graphical Interpretation of AccelerationAverage acceleration is the slope of the line connecting the initial and final velocities on the velocity-time graphInstantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph for the given value of time

1D motion: uniform velocityUniform velocity (shown by red arrows maintaining the same size)Acceleration equals zero

1D motion: constant (positive) accelerationVelocity and acceleration are in the same directionAcceleration is uniform (blue arrows maintain the same length)Velocity is increasing in time (red arrows are getting longer)

1D motion: constant (negative) accelerationVelocity and acceleration are in opposite directionsAcceleration is uniform (blue arrows maintain the same length)Velocity is decreasing (red arrows are getting longer)1D motion: constant acceleration

Our job: to find the equation for the position and velocity of the object to make predictions!10

1D motion with constant accelerationRecall that

We know that

We findvtv0

Sincextx011

1D motion with constant acceleration

12Summary of kinematic equations: 1D motion

acceleration is constant

displacement as a function of velocity and time

displacement as a function of time

velocity as a function of time

velocity as a function of displacement

average velocityDisplacement as a function of velocity

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Free fall - 1D motion with constant acceleration

14Free fall - 1D motion with constant acceleration0x123

0y123

All objects moving under the influence of only gravity are said to be in free fall

All objects falling near the earths surface fall with a constant acceleration

This acceleration is called gravitations acceleration, indicated by g and always points perpendicular to the earths surface y15accelerationdisplacement vs velocity and timedisplacement vs timevelocity vs timevelocity vs displacementaverage velocitydisplacement vs velocityFree fall - 1D motion with constant acceleration

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Case 1: zero initial velocity

y17

Case 2: NONzero initial velocity

y

yCase 1Case 218

Case 3: object thrown upward

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Case 4: object thrown upward

Free fallMass does not matter, if the air resistance is neglected

21Positive acceleration

22Negative acceleration

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1D motion with constant accelerationExample 1: A car is traveling with a constant speed v0. At some time, the driver puts on the brakes, which slows the car down at a rate of a. Find: how much farther does the car travel for time tf, before it stops completely.low long does it travel if the stopping distance is xf.

Given:v0=v0a=-ax0=0t0=0v=0Find:

1) xf=?, knowing tf.2) tf=?, knowing xf.