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Questions and Answers
What is the initial velocity (v0) of the pebble at the moment it is dropped?
The acceleration of the pebble is positive as it falls down.
False
What is the displacement of the pebble after three seconds?
-44.1 m
All objects in free fall descend under the constant acceleration of ________.
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Match the following terms with their definitions:
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What does acceleration represent in physics?
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The displacement of an object is calculated as the final position minus the initial position.
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What is the formula to calculate average acceleration?
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What does the displacement equation represent when a car travels at a constant velocity?
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Acceleration can be defined as the change in _____________ of an object in a given time interval.
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If a car experiences constant acceleration, the displacement is given by $x - x_0 = v_0 t + at^2$.
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If a car has an initial velocity of +10 m/s and a constant acceleration of 2 m/s², what will its final velocity be after 5 seconds?
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What happens to the displacement equation when the initial position is zero?
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Displacement is defined as the __________ position minus the __________ position.
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Displacement can also be calculated using the equation $x = x_0 + v_0 t + _____$.
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What is the final velocity of an object under constant acceleration after a certain time if its initial velocity is 15 m/s and it accelerates at 3 m/s² for 4 seconds?
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In a scenario where initial velocity and initial position are both zero, what does the displacement equation simplify to?
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Match the following variables with their meanings:
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What is the term that represents constant change in velocity?
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If a box has an initial velocity of +10 m/s and a constant acceleration of -1 m/s^2, its displacement after 10 seconds will be given by: $x = v_0 t + _____$.
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Match the following terms to their definitions:
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What is the simplified displacement equation when the initial position is set to zero?
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The alternate velocity equation v2 = v0^2 + 2ax can be used for three-dimensional motion.
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What is the total displacement of the box from its initial position after 10 seconds if the displacement calculation is 100 m + 1(-100 m)?
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The general displacement equation is given by x = x0 + v0t + ___t^2.
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If an airplane has an initial speed of +15 m/s and accelerates at +6 m/s² over 600 m, what is its final velocity?
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In the equation v = v0 + at, a represents the ___ of the object.
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Match the term with its definition:
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What is the significance of setting the initial velocity (v0) to zero in the equation v2 = v0^2 + 2ax?
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Study Notes
Equations of Motion
- Objective: Solve problems for objects with constant acceleration, linking displacement, velocity, acceleration, and time.
Key Kinematic Equations
- Acceleration (a) is the change in velocity (v) over time (t): ( a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t} ).
- Final velocity (v) can be calculated as: ( v = v_0 + at ), where:
- ( v_0 ): initial velocity (m/s)
- ( a ): acceleration (m/s²)
- ( t ): time (s)
Example of Constant Acceleration
- If a car has an initial velocity of +10 m/s and accelerates at 2 m/s² over 5 seconds, final velocity can be calculated as:
- ( v = +10 , \text{m/s} + (2 , \text{m/s}²)(5 , \text{s}) = +20 , \text{m/s} ).
Displacement and Its Equation
- Displacement (( \Delta x )) is the change in position: ( \Delta x = x - x_0 ).
- For constant velocity ( v_0 ): ( \Delta x = v_0 t ).
- With constant acceleration (( a )), the displacement equation becomes:
- ( \Delta x = v_0 t + \frac{1}{2} a t^2 ).
- Rearranged to solve for final position:
- ( x = x_0 + v_0 t + \frac{1}{2} a t^2 ).
Practical Example of Displacement
- A box on a conveyor with initial velocity of +10 m/s and acceleration of -1 m/s²:
- Over 10 seconds, total displacement is calculated using:
- ( x = 0 + (+10)(10) + \frac{1}{2}(-1)(10^2) = 100 - 50 = 50 ) meters.
Alternate Velocity Equation
- Alternate equation for one-dimensional motion with acceleration:
- ( v^2 = v_0^2 + 2ax ).
- This allows calculation of any variable (v, ( v_0 ), ( a ), or ( x )) if acceleration and other parameters are known.
- Simplifies to ( v^2 = 2ax ) when ( v_0 = 0 ).
Example of Finding Velocity
- If an airplane starts at +15 m/s, accelerates at +6 m/s² over 600 meters:
- Use: ( v^2 = (15 , \text{m/s})^2 + 2(6 , \text{m/s}²)(600 , \text{m}) ) to find final velocity.
Projectile Motion
- For objects in free fall, such as a pebble dropped from a height:
- Values are: ( v_0 = 0 , \text{m/s} ), ( a = -9.8 , \text{m/s}² ) (due to gravity), ( t = 3.0 , \text{s} ).
- Displacement (( y )) after 3 seconds is calculated as:
- ( y = v_0 t + \frac{1}{2} a t^2 ).
Free Fall Characteristics
- Constant acceleration due to gravity (approximately -9.8 m/s²).
- Free fall continues unless acted upon by external forces, like air resistance, which can lead to terminal velocity—the maximum velocity where forces balance.
Summary
- Objects in free fall experience constant acceleration due to gravity, unaffected unless external forces apply. Air resistance can ultimately oppose gravity and stabilize at terminal velocity.
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Description
Test your understanding of the equations of motion and kinematics in this quiz. You'll solve problems involving displacement, velocity, acceleration, and time for objects moving with constant acceleration. Be prepared to apply the formulas and concepts learned in this lesson.
