Define the term kinematics .

Kinematics is the branch of mathematics that models and analyses the motion of objects.

What is displacement ?

Displacement is the distance of an object in a particular direction ( positive or negative ) from a fixed point.

True or False? Displacement can be negative.

True. Displacement can be negative.

Velocity is the rate of change of displacement at time t .

What is speed in the context of kinematics?

In the context of kinematics, speed is the magnitude (absolute value) of velocity .

What is acceleration ?

Acceleration is the rate of change of velocity at time t .

True or False? A particle at rest always has zero acceleration .

False. A particle at rest has zero velocity , but may have non-zero acceleration.

What does " at rest " imply about a particle's velocity?

At rest implies that the particle's velocity is zero .

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

The gradient of a velocity-time graph represents acceleration .

True or False? Constant acceleration is always indicated on a velocity-time graph by a horizontal line .

False. Constant acceleration is not always indicated on a velocity-time graph by a horizontal line . Constant acceleration is indicated by any straight line on a velocity-time graph. A horizontal line on a velocity-time graph indicates constant velocity (as well as a constant acceleration of zero).

What does the area under a velocity-time graph represent?

The area under a velocity-time graph represents displacement .

True or False? Deceleration (slowing down) occurs when a particle's velocity and acceleration have the same sign .

False. Deceleration (slowing down) occurs when a particle's velocity and acceleration have different signs .

What does a velocity-time graph crossing the x -axis indicate?

A velocity-time graph crossing the x -axis indicates the object is stationary at that time.

True or False? Velocity is the antiderivative of acceleration .

True. Velocity is the antiderivative of acceleration .

What does the integral of velocity with respect to time represent?

The integral of velocity with respect to time represents displacement .

True or False? The distance travelled is always equal to the displacement .

False. The distance travelled is equal to the integral of the absolute value of velocity .

What is a boundary condition in kinematics?

A boundary condition is information given about an object at a specific time.

How can you find the constant of integration in kinematics problems?

The constant of integration in kinematics problems can be found by substituting known values from initial or boundary conditions .

True or False? The area under a velocity-time graph can be negative .

True. The area under a velocity-time graph can be negative , representing displacement in the negative direction .

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Define the term kinematics.
Kinematics is the branch of mathematics that models and analyses the motion of objects.
What is displacement?
Displacement is the distance of an object in a particular direction (positive or negative) from a fixed point.
True or False?
Displacement can be negative.
True.
Displacement can be negative.
What is velocity?
Velocity is the rate of change of displacement at time t.
What is speed in the context of kinematics?
In the context of kinematics, speed is the magnitude (absolute value) of velocity.
What is acceleration?
Acceleration is the rate of change of velocity at time t.
True or False?
A particle at rest always has zero acceleration.
False.
A particle at rest has zero velocity, but may have non-zero acceleration.
What does "at rest" imply about a particle's velocity?
At rest implies that the particle's velocity is zero.
What does the gradient of a velocity-time graph represent?
The gradient of a velocity-time graph represents acceleration.
True or False?
Constant acceleration is always indicated on a velocity-time graph by a horizontal line.
False.
Constant acceleration is not always indicated on a velocity-time graph by a horizontal line.
Constant acceleration is indicated by any straight line on a velocity-time graph.
A horizontal line on a velocity-time graph indicates constant velocity (as well as a constant acceleration of zero).
What does the area under a velocity-time graph represent?
The area under a velocity-time graph represents displacement.
True or False?
Deceleration (slowing down) occurs when a particle's velocity and acceleration have the same sign.
False.
Deceleration (slowing down) occurs when a particle's velocity and acceleration have different signs.
What does a velocity-time graph crossing the x-axis indicate?
A velocity-time graph crossing the x-axis indicates the object is stationary at that time.
When using calculus for kinematics, what is the equation for velocity in terms of displacement?
The equation for velocity in terms of displacement is $v = \frac{d s}{d t}$ .
Velocity is the derivative of displacement.
When using calculus for kinematics, what is the equation for acceleration in terms of velocity?
The equation for velocity in terms of displacement is $a = \frac{d v}{d t}$ .
Acceleration is the derivative of velocity.
Define the second derivative of displacement?
The second derivative of displacement is acceleration.
This can be written as $a = \frac{d^{2} s}{d t^{2}}$ .
True or False?
Velocity is the antiderivative of acceleration.
True.
Velocity is the antiderivative of acceleration.
What does the integral of velocity with respect to time represent?
The integral of velocity with respect to time represents displacement.
True or False?
The distance travelled is always equal to the displacement.
False.
The distance travelled is equal to the integral of the absolute value of velocity.
What is a boundary condition in kinematics?
A boundary condition is information given about an object at a specific time.
What is an initial condition in kinematics?
An initial condition is information given about an object at time $t = 0$ .
An initial condition is a type of boundary condition.
What does $\int_{t_{1}}^{t_{2}} v (t) d t$ represent in kinematics?
$\int_{t_{1}}^{t_{2}} v (t) d t$ represents the displacement of the particle between times t₁ and t₂.
What does $\int_{t_{1}}^{t_{2}} |v (t)| d t$ represent in kinematics?
$\int_{t_{1}}^{t_{2}} |v (t)| d t$ represents the distance travelled by the particle between times t₁ and t₂.
How can you find the constant of integration in kinematics problems?
The constant of integration in kinematics problems can be found by substituting known values from initial or boundary conditions.
True or False?
The area under a velocity-time graph can be negative.
True.
The area under a velocity-time graph can be negative, representing displacement in the negative direction.

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Kinematics (DP IB Analysis & Approaches (AA))

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1. Number & Algebra

Number & Algebra Toolkit

Exponentials & Logs

Sequences & Series

Simple Proof & Reasoning

Proof by Induction & Contradiction

Binomial Theorem

Permutations & Combinations

Complex Numbers

Further Complex Numbers

Systems of Linear Equations

2. Functions

Linear Functions & Graphs

Quadratic Functions & Graphs

Functions Toolkit

Other Functions & Graphs

Reciprocal & Rational Functions

Transformations of Graphs

Polynomial Functions

Inequalities

Modulus Functions & Further Transformations

3. Geometry & Trigonometry

Geometry Toolkit

Geometry of 3D Shapes

Trigonometry

The Unit Circle & Exact Values

Trigonometric Functions & Graphs

Trigonometric Equations & Identities

Inverse & Reciprocal Trigonometric Functions

Trigonometric Proof & Equation Strategies

Vector Properties

Vector Equations of Lines

Vector Planes

4. Statistics & Probability

Statistics Toolkit

Correlation & Regression

Probability

Discrete Random Variables

Binomial Distribution

Normal Distribution

Continuous Random Variables

5. Calculus

Differentiation

Techniques & Applications of Differentiation

Integration

Techniques & Applications of Integration

Optimisation

Kinematics

Basic Limits & Continuity

Further Differentiation

Further Integration

Differential Equations

Maclaurin Series

Limits using l'Hôpital's Rule & Maclaurin Series