Chapter 2 – Motion in a Straight Line (Lecture Summary)

Vocabulary flashcards covering fundamental terms and concepts from Chapter 2: Motion in a Straight Line, including definitions of kinematic quantities, graphical interpretations, key equations, and illustrative applications such as free fall, stopping distance, and reaction time.

Motion

Change in position of an object with time.

Point Object Approximation

Treating a body as a single point when its size is negligible compared to the distance travelled.

Rectilinear Motion

Motion of an object along a straight line.

Kinematics

Branch of mechanics that describes motion without dealing with its causes.

Displacement

Vector quantity representing change in position; has magnitude and direction.

Distance (Path Length)

Total length of the path travelled; always non-negative scalar.

Average Velocity

Displacement divided by the time interval: Δx / Δt.

Instantaneous Velocity

Limit of average velocity as Δt → 0; v = dx/dt.

Average Speed

Total path length divided by total time; ≥ |average velocity|.

Instantaneous Speed

Magnitude of instantaneous velocity.

Average Acceleration

Change in velocity divided by the time interval: Δv / Δt.

Instantaneous Acceleration

Limit of average acceleration as Δt → 0; a = dv/dt.

Sign Convention

Choice of positive direction (usually rightward or upward) that sets algebraic signs for x, v, and a.

Uniform Motion

Motion with constant velocity (zero acceleration).

Constant (Uniform) Acceleration

Motion where acceleration has constant magnitude and direction.

Position–Time (x-t) Graph

Graph showing position versus time; slope gives instantaneous velocity.

Velocity–Time (v-t) Graph

Graph showing velocity versus time; slope gives instantaneous acceleration.

Acceleration–Time (a-t) Graph

Graph showing acceleration versus time.

Slope of x-t Graph

Tangent’s slope equals instantaneous velocity at that instant.

Slope of v-t Graph

Tangent’s slope equals instantaneous acceleration.

Area under v-t Graph

Represents displacement during the chosen time interval.

Kinematic Equation 1

v = v₀ + at (relates velocities, acceleration, and time).

Kinematic Equation 2

x = v₀t + ½at² (relates displacement, time, initial velocity, and acceleration).

Kinematic Equation 3

v² = v₀² + 2a(x – x₀) (relates velocities, displacement, and acceleration).

Free Fall

Motion under gravity alone; constant downward acceleration g ≈ 9.8 m s⁻².

Galileo’s Law of Odd Numbers

For free fall, distances in equal successive times are in ratio 1:3:5:7…

Stopping Distance

Distance a vehicle travels after brakes are applied: d_s = v₀² / (2a) with a as magnitude of deceleration.

Reaction Time

Interval between perception and action; can be estimated from distance fallen by a dropped ruler.

Differentiation in Kinematics

Process of obtaining velocity and acceleration from position: v = dx/dt, a = dv/dt.

Integration in Kinematics

Finding position from velocity or velocity from acceleration by integrating with respect to time.

Speeding Up vs Slowing Down

Object speeds up if a and v have same sign; slows down if signs are opposite.

Zero Velocity ≠ Zero Acceleration

An object can have v = 0 yet a ≠ 0 (e.g., at the peak of upward projectile motion).

Stopping Distance–Speed Relation

Stopping distance is proportional to the square of initial speed (d_s ∝ v₀²).