Physics Class on Vectors and Motion
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Questions and Answers

What does the slope of a velocity-time graph represent?

  • Speed
  • Displacement
  • Distance
  • Acceleration (correct)

Which of the following is NOT a vector quantity?

  • Acceleration
  • Velocity
  • Mass (correct)
  • Displacement

Which of the following methods can be used to add vectors?

  • All (correct)
  • Component Method
  • Triangle Law
  • Parallelogram Law

What is the result of the cross product of two vectors?

<p>A vector perpendicular to both original vectors (D)</p> Signup and view all the answers

Splitting of vectors into two components along any two perpendicular axes is called...

<p>Resolution (D)</p> Signup and view all the answers

What is the SI unit for acceleration?

<p>m/s² (D)</p> Signup and view all the answers

What is the average speed of a car that travels 120 km in 2 hours?

<p>60 km/h (B)</p> Signup and view all the answers

Which of the following quantities is a vector?

<p>Velocity (B)</p> Signup and view all the answers

What is the horizontal component of a projectile launched at an angle of 30 degrees with an initial velocity of 10 m/s?

<p>8.66 m/s (D)</p> Signup and view all the answers

What does the slope of a position-time graph represent?

<p>Velocity (A)</p> Signup and view all the answers

What is the maximum height reached by a projectile launched with an initial velocity of 30 m/s at an angle of 60 degrees?

<p>45 m (D)</p> Signup and view all the answers

If two vectors A and B are parallel, what is their cross product?

<p>Zero (A)</p> Signup and view all the answers

How long does it take for a ball to hit the ground if dropped from a height of 100 meters (using $g = 10 m/s²$)?

<p>5 seconds (D)</p> Signup and view all the answers

Which statement correctly describes scalar quantities?

<p>Have only magnitude (D)</p> Signup and view all the answers

What is the minimum possible magnitude of the resultant of two vectors with magnitudes 5 units and 3 units?

<p>2 units (C)</p> Signup and view all the answers

What is the acceleration of a 5 kg object acted upon by a net force of 20 N?

<p>4 m/s² (B)</p> Signup and view all the answers

How is displacement different from distance?

<p>Distance is the total path length while displacement is the net change in position. (C)</p> Signup and view all the answers

What is the displacement vector in component form for a person walking 2 km north, 3 km east, and 1 km south?

<p>(1 km, 2 km) (C)</p> Signup and view all the answers

If two vectors A and B have magnitudes of 5 and 12 units and an angle of 60 degrees between them, what is the magnitude of their resultant?

<p>13 units (A)</p> Signup and view all the answers

What is the average velocity of an object moving from position x = 2 m to x = -3 m in 5 seconds?

<p>-1 m/s (B)</p> Signup and view all the answers

How far does a car travel if it accelerates uniformly from rest to 25 m/s in 10 seconds?

<p>125 m (A)</p> Signup and view all the answers

What determines the direction of the resultant of two vectors when added graphically?

<p>Drawing a line from the tail of the first vector to the head of the second (D)</p> Signup and view all the answers

Under what conditions are the kinematic equations valid?

<p>When acceleration is constant (A)</p> Signup and view all the answers

Flashcards

Vector Quantities

Quantities that have both magnitude and direction.

Scalar Quantities

Quantities that have only magnitude and no direction.

Acceleration

The rate of change of velocity with time.

Distance

The total path length travelled.

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Displacement

The net change in position from the starting point to the ending point.

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Velocity

The slope of a position-time graph.

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Vector Subtraction

To subtract a vector, you can add its opposite.

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Cross Product of Parallel Vectors

The cross product of two parallel vectors is always 0.

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Reference Frame

A reference frame provides a consistent and unambiguous way to measure and describe the position and motion of an object.

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Kinematic Equations

The kinematic equations describe the motion of an object under constant acceleration.

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Velocity-Time Graph Slope

The slope of a velocity-time graph represents the acceleration of an object.

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Displacement-Time Graph Slope

The slope of a displacement-time graph represents the velocity of an object.

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Vector Resolution

Breaking down a vector into its components along two perpendicular axes. Helps to analyze and calculate forces and motion.

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What does the slope of a velocity-time graph represent?

The slope of a velocity-time graph represents the rate of change in velocity. This rate of change is defined as acceleration.

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Resolution of a vector

The splitting of a vector into its horizontal and vertical components.

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Is velocity a vector quantity?

In physics, vectors are quantities that have both magnitude and direction. Velocity is a vector quantity because it describes both the speed and direction of an object's motion.

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Adding vectors

The process of combining vectors to find their resultant vector. This can be done using the Triangle Law, Parallelogram Law, or Component Method.

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Average Speed

The average speed is calculated by dividing the total distance traveled by the total time taken. It represents the overall rate of movement over a particular period.

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What is Velocity?

The velocity of an object is its rate of change in position with respect to time. It includes both the magnitude (speed) and direction of motion.

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Centripetal Acceleration

Centripetal acceleration is the acceleration that is directed towards the center of a circular path. It is responsible for keeping an object moving in a circular path.

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Maximum Height of a Projectile

The maximum height reached by a projectile is the highest point it attains during its flight. It depends on the initial vertical velocity and the acceleration due to gravity.

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Range of a Projectile

The range of a projectile is the horizontal distance it travels from its launch point to the point where it lands. It is determined by the initial speed and the launch angle.

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Unit Vector

The unit vector of a vector is a vector with the same direction, but with a magnitude of 1. To find the unit vector, divide the vector by its own magnitude.

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Dot Product of Vectors

The dot product of two vectors is a scalar quantity that is equal to the product of the magnitudes of the vectors and the cosine of the angle between them.

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Study Notes

Matching (1)

  • Velocity matches with $i)$ $m/s$
  • Acceleration matches with $iii)$ $m/s^2$
  • Force matches with $iv)$ $N$
  • Mass matches with $ii)$ $kg$

Fill in the Blank (2)

  • A vector has both magnitude and direction
  • To subtract a vector, you can add its negative
  • The cross product of two parallel vectors is always zero
  • The slope of a position-time graph represents velocity

Short Answer (8)

  • List and define types of physical quantity depending on direction and give two examples in each.
    • Scalar quantities have only magnitude (e.g., mass, speed, distance).
    • Vector quantities have both magnitude and direction (e.g., force, velocity, displacement).
  • If vector A has a magnitude of 5 units and vector B has a magnitude of 3 units, what is the maximum and minimum possible magnitude of their resultant?
    • Maximum: 8 units (when vectors point in the same direction).
    • Minimum: 2 units (when vectors point in opposite directions).
  • Define acceleration and give its SI unit.
    • Acceleration is the rate of change of velocity. SI unit: $m/s^2$.
  • Why is it important to define a reference frame when describing motion?
    • A reference frame provides a coordinate system for defining the position and motion of objects.
  • A car is traveling at a constant speed of 60 km/h. Does it have a constant velocity? Explain.
    • No, constant speed does not imply constant velocity. Constant velocity requires both constant magnitude and direction of velocity, which may not be present with constant speed. For example, a car driving around a curve has constant speed but changing velocity.
  • Explain the difference between distance and displacement.
  • How can you determine the direction and the resultant of two vectors graphically?
  • What are the kinematic equations, and under what conditions are they valid?
    • The kinematic equations describe the motion of objects with constant acceleration. They are valid when the acceleration is constant.

Work out (24)

  • A person walks 5 meters east and then 3 meters west. What is their total distance traveled? What is their displacement?
    • Total distance: 8 meters
    • Displacement: 2 meters East
  • An object moves from position $x = 2$ m to $x = -3$ m in 5 seconds. What is its average velocity?
    • Average velocity: -1 m/s
  • If $\vec{A} = 2\vec{i} + 4\vec{j} + 7\vec{k}$ and $\vec{B} = 3\vec{i} + 4\vec{j} + 7\vec{k}$. Find the resultant and its magnitude of the two vectors. -Resultant: $5 \vec{i} + 8\vec{j} + 14\vec{k}$
    • Magnitude: $\sqrt{5^2 + 8^2 + 14^2} = \sqrt{25+64+196} = \sqrt{285}$
  • If $\vec{A} = 4\vec{i} - 4\vec{j}$, $\vec{B} = 3\vec{i} + 7\vec{j}$ and $\vec{c} = 11\vec{i} - 4\vec{j}$. Find the values of a, b & c such that $a\vec{A} + b\vec{B} + c\vec{c} = \vec{0}$.
    • $a = 1, b = -2, c = 1$

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Description

Test your understanding of vectors and their applications in physics with this quiz. Explore concepts such as slope in velocity-time graphs and vector addition methods. Perfect for students looking to reinforce their knowledge in motion and vectors.

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