Kinematics ✏ AP Physics 1

Rucete ✏ AP Physics 1 In a Nutshell

2. Kinematics

This chapter explores the descriptive study of motion, known as kinematics. It covers average and instantaneous velocity, acceleration, free fall, projectile motion, graphical analysis, and uniform circular motion. Kinematics is foundational for analyzing how objects move in both one and two dimensions.

Average and Instantaneous Motion

• Displacement is a vector (has direction); distance is a scalar.

• Average velocity = displacement / time (vector quantity).

• Instantaneous velocity is velocity at a specific moment; shown on a speedometer.

• If velocity is constant, average = instantaneous velocity.

• On a position vs. time graph, slope = velocity.

Acceleration

• Acceleration = change in velocity / time (vector quantity).

• Uniform acceleration → velocity vs. time graph is a straight line (slope = acceleration).

• Displacement = area under the velocity vs. time graph (triangle + rectangle).

• Key formulas for uniformly accelerated motion:

 1. v = vi + at

 2. x = vit + ½at²

 3. v² = vi² + 2aΔx (time-independent)

• Average velocity under constant acceleration: (vi + vf)/2

Accelerated Motion Due to Gravity

• Free fall acceleration (g) = 9.8 m/s² downward.

• Upward motion: vi positive, acceleration negative.

• Downward motion: vi negative, acceleration also negative.

• Gravity always acts downward, even at peak height of projectile.

• Motion direction and sign of acceleration determine speeding up or slowing down.

Graphical Analysis of Motion

• Displacement vs. time: slope = velocity.

• Velocity vs. time: slope = acceleration; area under graph = displacement.

• Graphs help visualize changes in motion (e.g., speeding up, slowing down).

Relative Motion

• All motion is measured relative to a chosen frame of reference.

• Relative velocity between two objects depends on the observer’s frame.

• Example: A car moving at 30 km/h relative to a truck moving at 20 km/h in the same direction has a relative velocity of 10 km/h.

• Vector subtraction is used:  V_{A rel to B} = V_A – V_B

Horizontally Launched Projectiles

• Horizontal and vertical motions are independent.

• Horizontal velocity is constant (no acceleration).

• Vertical motion is free fall with a = g downward.

• Time of flight is determined by vertical motion:  y = ½gt² → t = √(2y/g)

• Horizontal range = v_x × t

Projectiles Launched at an Angle

• Break initial velocity into components:

 v_x = v·cos(θ), v_y = v·sin(θ)

• Horizontal motion: constant velocity.

• Vertical motion: upward motion slows, stops at peak, then accelerates downward.

• Total time in air = 2t_up = 2(v_y / g)

• Maximum height = v_y² / (2g)

• Range = v²·sin(2θ) / g

In a Nutshell

Kinematics describes how objects move using vectors, equations, and graphs. It includes the analysis of velocity, acceleration, free fall, and projectile motion. Understanding how to break motion into components and apply consistent vector directions is essential for predicting and interpreting physical systems in both one and two dimensions.