Motion in One Dimension – Kinematics Vocabulary

Vocabulary flashcards summarizing key terms and definitions from the lecture on motion in one dimension and related kinematic concepts.

Kinematics

Branch of mechanics that studies motion of objects without considering the causes of motion.

Motion

State in which a body changes its position with time relative to an observer.

Rest

State in which a body does not change its position with time relative to its surroundings.

Rectilinear Motion

Motion of a particle along a straight line.

Point Mass Object (Particle)

Body whose size is negligible compared with the distance it moves, allowing it to be treated as a single point.

Frame of Reference

Set of three mutually perpendicular axes with an origin and a clock, relative to which motion parameters are described.

One-Dimensional Motion

Motion where only one coordinate (x, y, or z) changes with time.

Two-Dimensional Motion

Motion where exactly two coordinates change with time.

Three-Dimensional Motion

Motion in which all three spatial coordinates change with time.

Distance

Total length of the path travelled by a particle; a scalar quantity, always positive or zero.

Displacement

Shortest directed distance from initial to final position of a particle; a vector that can be positive, negative, or zero.

Position Vector

Vector that locates a point in space relative to an origin; difference of two position vectors gives displacement.

Speed

Rate at which distance is covered with time; scalar and never negative.

Average Speed

Total distance travelled divided by total time taken.

Instantaneous Speed

Speed of a particle at a particular instant; magnitude of instantaneous velocity.

Velocity

Rate of change of displacement with time; a vector that can be positive, negative, or zero.

Average Velocity

Total displacement divided by total time taken.

Instantaneous Velocity

Velocity of a particle at a specific instant of time; limit of average velocity as Δt → 0.

Relative Velocity

Velocity of one object as observed from another, given by VAB = VA − V_B.

Relative Acceleration

Acceleration of one body with respect to another, aAB = aA − a_B.

Rain-Man Relative Velocity

Apparent velocity of rain to a walking observer: VRM = VR − V_M (vector subtraction).

Umbrella Angle

Tilt angle θ where tanθ = VM / VR to keep dry when rain falls vertically and the observer moves horizontally.

River-Boat Relative Velocity

Ground velocity of a swimmer/boat: VM = VMR + VR, where VMR is velocity in still water and V_R is river current.

Downstream Velocity

When swimmer moves with current: Vdown = VMR + V_R (magnitude increases).

Upstream Velocity

When swimmer moves against current: Vup = VMR − V_R (magnitude decreases).

Shortest Path Across River

Swim at an angle so that cross-stream component cancels drift (VMR sinθ = VR); results in minimum displacement.

Minimum Time Across River

Swim perpendicular to current (θ = 0) so that cross-river component is maximized; drift occurs but crossing time is least.

Acceleration

Rate of change of velocity with time; vector with direction of Δv.

Average Acceleration

Total change in velocity divided by total time interval.

Instantaneous Acceleration

Acceleration at a specific instant; derivative dv/dt.

Positive Acceleration

Velocity magnitude increases with time.

Negative Acceleration (Retardation)

Velocity magnitude decreases with time.

First Equation of Motion

v = u + at for constant acceleration.

Second Equation of Motion

s = ut + ½ a t² for constant acceleration.

Third Equation of Motion

v² = u² + 2 a s for constant acceleration.

Free Fall

Motion under gravity alone (a = +g downward), initial u = 0 when dropped.

Vertical Projection Upwards

Motion against gravity (a = −g); maximum height when v = 0.

Time of Flight (Vertical)

Total time to rise and fall back: T_total = 2u/g.

Maximum Height

h_max = u² / (2g) reached in time T = u/g.

S-t Graph Slope

Slope of displacement-time graph equals instantaneous velocity.

V-t Graph Slope

Slope of velocity-time graph equals acceleration.

Area under V-t Graph

Gives displacement (or distance if all velocities are positive).

Area under a-t Graph

Represents change in velocity over the time interval.

Uniform Velocity

Constant speed in a fixed direction; zero acceleration.

Uniform Acceleration

Constant acceleration; velocity changes linearly with time.