Motion In One Dimension - Lecture Notes

Flashcards covering motion descriptors, definitions of distance, displacement, speed, velocity, acceleration, and the four kinematic equations for uniform acceleration.

How is motion defined in the transcript?

Motion is defined as the change of position of an object in a specific span of time relative to an observer.

What are the two fundamental requirements for motion?

Motion requires position and time.

What is the SI unit for time and how is it usually symbolized?

The SI unit for time is seconds ($s$) and it is usually noted by $t$.

What is the difference between distance and displacement?

Distance describes how far an object has traveled (total length), while displacement is the length and direction of the line connecting the initial position to the final position.

Under what specific condition can distance and displacement be equal?

They can only be equal if the object in motion travels in one direction only and does not return to its original position.

What are the types of quantities for speed and velocity?

Speed is a scalar quantity, while velocity is a vector quantity.

How is velocity defined differently from speed?

Speed is the rate of change in position, while velocity is the rate of change in position with respect to a reference point, where direction is important.

What is defined as the rate of change in an object's velocity per elapsed time?

Acceleration.

What is the SI unit for acceleration?

The SI unit is $m/s^2$.

What are the three ways to identify that an object is accelerating?

An object is accelerating if (1) the magnitude of velocity changes, (2) the direction of motion changes, or (3) both magnitude and direction change.

What does negative acceleration (deceleration) indicate about an object's motion?

It indicates that acceleration ($a$) and velocity ($v$) are in opposite directions, and the object is slowing down.

What does it mean for motion to be 'relative'?

It means that an object that is moving for one observer might not be moving relative to another observer.

What is the mathematical definition of average velocity ($v_{ave}$)?

$$v_{ave} = \frac{d}{t}$$

What does instantaneous velocity represent?

The velocity of an object in a single point of time (an instant).

In a position-time graph, what determines the instantaneous velocity?

The slope of the graph at a specific point.

How is instantaneous velocity ($v_{ins}$) solved using calculus?

By taking the derivative of the position-time equation: $v_{ins} = \frac{dx}{dt}$

How is instantaneous acceleration ($a_{ins}$) calculated in calculus?

By taking the derivative of the velocity equation: $a_{ins} = \frac{dv}{dt}$

State the first Constant Acceleration Equation (Displacement-Independent Equation).

$$v = v_0 + at$$

State the second Constant Acceleration Equation (Acceleration-Independent Equation).

$$\Delta x = \frac{v + v_0}{2} t$$

State the third Constant Acceleration Equation (Final Velocity-Independent Equation).

$$\Delta x = v_0t + \frac{1}{2} at^2$$

State the fourth Constant Acceleration Equation (Time-Independent Equation).

$$v^2 = v_0^2 + 2a\Delta x$$

What is the 'implicit' given value when a problem states an object 'starts from rest'?

The initial velocity ($v_0$) is $0\,m/s$.

When does constant acceleration occur?

When the rate of change in the velocity of an object is the same throughout the travel.