AP Physics C: Mechanics:: Kinematics

What is the difference between DISTANCE and DISPLACEMENT?

- **A)** Distance and displacement are always exactly equal to each other, with no meaningful difference between them
- **B)** DISTANCE is the TOTAL PATH LENGTH traveled (a scalar, always positive), while DISPLACEMENT is the STRAIGHT-LINE change in position from start to end (a vector, which can be zero even if distance traveled is large)
- **C)** Distance is a vector quantity, while displacement is a scalar quantity (the reverse of the actual classification of these two quantities)
- **D)** This distinction has no actual relationship to the difference between total path length and straight-line position change

What is the difference between AVERAGE SPEED and AVERAGE VELOCITY?

- **A)** Average speed and average velocity are always exactly equal to each other, with no meaningful distinction between them
- **B)** Average velocity is always a scalar quantity, while average speed is always a vector quantity (the reverse of the actual classification)
- **C)** This distinction has no actual relationship to whether distance or displacement is used in the calculation
- **D)** AVERAGE SPEED is total DISTANCE divided by total time (a scalar), while AVERAGE VELOCITY is total DISPLACEMENT divided by total time (a vector) -- these can differ significantly if the path is not a straight line

What is ACCELERATION, and how is it mathematically defined in terms of VELOCITY and TIME?

- **A)** This concept has no actual mathematical relationship to how velocity changes over time
- **B)** The RATE OF CHANGE of velocity with respect to time (a = delta v / delta t) -- acceleration occurs whenever an object's speed changes, its direction changes, or BOTH
- **C)** Acceleration can only occur when an object's SPEED changes, never when only its DIRECTION changes
- **D)** Acceleration is defined as the rate of change of POSITION with respect to time, identical to the definition of velocity

Why can an object be ACCELERATING even if its SPEED remains PERFECTLY CONSTANT, such as a car moving at a constant speed around a circular curve?

- **A)** An object moving at constant speed can NEVER be accelerating under any circumstances, contradicting the actual definition of acceleration as a vector-based quantity
- **B)** Acceleration requires ONLY a change in speed, with direction changes never actually counting as acceleration
- **C)** Because VELOCITY is a vector (having both magnitude AND direction), a change in DIRECTION alone (even with constant speed) still counts as a change in velocity, and therefore still constitutes acceleration
- **D)** This concept has no actual relationship to why direction changes alone can constitute acceleration

What does a POSITION-VERSUS-TIME graph's SLOPE at any given point represent about an object's motion?

- **A)** The slope of a position-versus-time graph at any point represents the object's INSTANTANEOUS VELOCITY at that moment
- **B)** A position-versus-time graph's slope always represents the TOTAL DISTANCE traveled, rather than an instantaneous rate of change
- **C)** This concept has no actual relationship between a position-time graph's slope and the object's velocity
- **D)** The slope of a position-versus-time graph represents the object's ACCELERATION, rather than its velocity

What does a VELOCITY-VERSUS-TIME graph's SLOPE at any given point represent about an object's motion?

- **A)** A velocity-versus-time graph's slope always represents the object's total DISPLACEMENT, rather than an instantaneous rate of change
- **B)** This concept has no actual relationship between a velocity-time graph's slope and the object's acceleration
- **C)** The slope of a velocity-versus-time graph represents the object's POSITION, rather than its acceleration
- **D)** The slope of a velocity-versus-time graph at any point represents the object's INSTANTANEOUS ACCELERATION at that moment

What does the AREA UNDER a VELOCITY-VERSUS-TIME graph, between two points in time, represent about an object's motion during that interval?

- **A)** The area under a velocity-versus-time graph between two times represents the object's DISPLACEMENT during that time interval
- **B)** The area under a velocity-time graph always represents the object's INSTANTANEOUS speed at a single point, rather than displacement over an interval
- **C)** The area under a velocity-time graph represents the object's ACCELERATION during that interval, rather than its displacement
- **D)** This concept has no actual relationship between the area under a velocity-time graph and an object's displacement

What are the standard KINEMATIC EQUATIONS used to describe motion, and under what specific CONDITION do these particular equations apply?

- **A)** Kinematic equations require that VELOCITY (rather than acceleration) remain constant throughout the motion
- **B)** The standard kinematic equations apply to ANY type of motion, including motion with rapidly CHANGING (non-constant) acceleration
- **C)** A set of equations relating position, velocity, acceleration, and time; these standard equations apply specifically when ACCELERATION IS CONSTANT (uniform) throughout the motion
- **D)** This concept has no actual relationship to a specific condition (constant acceleration) required for these equations to apply