Physics Chapter on Measurement and Vectors

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Questions and Answers

Which of the following best describes precision?

The error margin of a measurement
Consistency in repeated measurements (correct)
Average of all measurements taken
Closeness to the true value

What does accuracy refer to in measurements?

The closeness of a measurement to the true value (correct)
The repeatability of multiple measurements
The deviation of measurements from each other
The consistency of measurements over time

What characterizes a systematic error?

It averages out to zero over multiple measurements
It varies randomly and inconsistently
It is caused by predictable fluctuations in measurement
It deviates consistently from the true value by a fixed amount (correct)

What does vector addition involve?

Combining two or more vectors to obtain a vector sum (A) Signup and view all the answers

Which of the following describes random errors?

They can be either positive or negative and do not repeat consistently (A) Signup and view all the answers

What does the area under the velocity-time graph represent in the context of free fall?

The total distance traveled by the object. (D) Signup and view all the answers

What is the effect of gravity on the velocity of an object in free fall?

It increases the velocity by $9.8 m/s^2$. (D) Signup and view all the answers

How is the vector sum obtained in vector addition?

By placing vectors head to tail and drawing from the free tail to the free head (C) Signup and view all the answers

In a downward motion under gravity, how is velocity defined?

Positive when falling and negative when rising. (B) Signup and view all the answers

Which of the following is NOT a characteristic of a vector?

It can be expressed as a scalar (B) Signup and view all the answers

What geometric shapes can be formed when analyzing the area under a velocity-time graph for free fall?

Rectangles and triangles. (B) Signup and view all the answers

In projectile motion launched at an angle, what components are present in the initial motion?

Both vertical and horizontal components. (B) Signup and view all the answers

What is the velocity of an object at its highest point during free fall?

$0 m/s$. (D) Signup and view all the answers

What characterizes projectile motion that is launched horizontally?

It has a constant horizontal takeoff speed. (B) Signup and view all the answers

What is the formula for calculating the horizontal distance covered by a projectile launched horizontally?

$d_x = v_x * t$ (A) Signup and view all the answers

What happens to the vertical velocity of a projectile launched at an angle over time?

It decreases due to gravity. (C) Signup and view all the answers

Which statement correctly describes the concept of range in projectile motion?

It refers to the horizontal distance covered by an object. (C) Signup and view all the answers

What is the proper format for scientific notation?

a x 10^b (C) Signup and view all the answers

What is the equation used to calculate the distance covered by an object moving at a constant speed?

ⅆ = 𝑣𝑡 (C) Signup and view all the answers

Which formula calculates the final velocity of an object under constant acceleration?

𝑣𝐹 = 𝑣𝑖 + 𝑎𝑡 (D) Signup and view all the answers

What is true about the kinematic equations?

They describe the motion of an object at constant acceleration. (D) Signup and view all the answers

In projectile motion, how are the horizontal and vertical motions characterized?

They are completely independent of each other. (B) Signup and view all the answers

Which formula would you use to find the distance when the initial velocity, final velocity, and acceleration are known?

𝑣𝐹2 = 𝑣𝑖2 + 2𝑎ⅆ (C) Signup and view all the answers

How is time calculated when distance and initial velocity are known?

𝑡 = rac{−(−𝑣𝑖) ± √[(−𝑣𝑖)2 − 4(−𝑎)(ⅆ)]}{2(−𝑎)} (D) Signup and view all the answers

What is a characteristic of projectile motion?

It maintains a constant horizontal velocity. (A) Signup and view all the answers

What happens to the vertical motion of a projectile?

It is independent from the horizontal motion. (C) Signup and view all the answers

What is a scalar quantity?

A quantity described only by magnitude (A) Signup and view all the answers

Which formula represents the resultant displacement for perpendicular vectors?

$d^2 = v_1^2 + v_2^2$ (C) Signup and view all the answers

What is instantaneous speed?

The speed of an object at a particular moment in time (A) Signup and view all the answers

How is average velocity calculated?

$ar{v} = rac{d_{ ext{total}}}{t_{ ext{total}}}$ (B) Signup and view all the answers

What does the area under a velocity vs. time graph represent?

Displacement (B) Signup and view all the answers

What is the formula for calculating resultant velocity from two vectors?

$v = ext{sqrt}(v_1^2 + v_2^2)$ (B) Signup and view all the answers

Which of the following statements is true regarding displacement?

Displacement is the shortest distance to the final position. (C) Signup and view all the answers

Which term accurately defines acceleration?

Change in velocity over time (B) Signup and view all the answers

What does the scalar speed of an object quantify?

The total distance covered in a specific time (C) Signup and view all the answers

What formula represents instantaneous acceleration?

$a = ext{lim}_{ riangle t o 0} rac{ riangle d}{ riangle t}$ (D) Signup and view all the answers

Which of the following accurately describes free fall?

An object moving only under the influence of gravity. (B) Signup and view all the answers

What is the primary difference between distance and displacement?

Distance is the total path traveled; displacement is the shortest direct line. (B) Signup and view all the answers

Which of the following is NOT a characteristic of a vector quantity?

Only described by a numerical value (C) Signup and view all the answers

How do you obtain the components of a vector in terms of angle $\theta$?

$x = V \cos(\theta)$ and $y = V \sin(\theta)$ (D) Signup and view all the answers

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Study Notes

Accuracy and Precision

Accuracy: Closeness of a measurement to the true or accepted value.
Precision: Consistency of repeated measurements, independent of accuracy.

Systematic and Random Errors

Systematic Error: Deviates from true value by a fixed amount; consistent in repeated measurements.
Random Error: Varies unpredictably; inconsistent in magnitude and direction, often caused by environmental variations.

Scientific Notation

Format expressed as ( a \times 10^b ), where ( b ) represents the exponent ensuring the proper mathematical representation of a number.

Scalars and Vectors

Scalar: Quantity described only by magnitude (e.g., speed, mass, time).
Vector: Quantity with both magnitude and direction (e.g., velocity, force).

Vector Addition

Vector Addition: Combining two or more vectors to form a resultant vector, achieved using the head-to-tail method.
Methods for Vector Addition:
- Graphical Method: Drawing vectors on a graph and summing with head-to-tail alignment.
- Trigonometric Method: Using right triangle properties to calculate the resultant vector.

Motion Concepts

Distance: Total path traveled, regardless of direction.
Displacement: Movement from initial to final position, defined as the shortest distance in a specific direction.

Velocity and Speed

Velocity: Speed with a directional component; specified at any moment.
Average Velocity: Total displacement over total time.
Instantaneous Velocity: Velocity at a specific moment in time.

Acceleration

Defined as the change in velocity over time; can indicate speeding up or slowing down.
Instantaneous Acceleration: Acceleration at a specific instant during motion.

Free Fall

Describes an object moving solely under gravity's influence, accelerating downward at approximately ( -9.8 , \text{m/s}^2 ).
Velocity decreases as an object rises, becomes zero at the peak height, then increases as it falls.

Graphical Interpretation of Motion

Displacement is represented as the area under velocity vs. time curves.
Velocity can be positive or negative based on the direction of motion relative to a reference point.

Kinematic Equations

A set of equations used to describe motion with constant acceleration.
Key equations include:
- ( v_f = v_i + at )
- ( d_T = v_i t + \frac{1}{2}at^2 )
- ( v_f^2 = v_i^2 + 2ad )

Projectile Motion

Describes the motion of objects traveling in 2D, combining horizontal (constant velocity) and vertical (accelerated motion) components.
Two types of projectile motion:
- Launched Horizontally: Maintains constant horizontal speed while accelerating vertically.
- Launched at an Angle: Has both horizontal and vertical components from the start.

Formulas Relevant to Projectile Motion

Horizontal motion: ( d_x = v_x t )
Vertical motion under gravity: ( d_y = \frac{1}{2}gt^2 ), where ( g ) approximates ( 9.8 , \text{m/s}^2 ).

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