A particle starts from rest at the origin with an...

A particle starts from rest at the origin with an acceleration vector that has magnitude $4 \mathrm{~m} / \mathrm{s}^{2}$ and direction $30^{\circ}$ above the positive $x$ axis. (a) What are the components of its velocity vector $20 \mathrm{~s}$ later? (b) What is the particle's position at that time?

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Key Concepts

Constant Acceleration

This concept involves the study of objects moving with an unchanging acceleration. Under constant acceleration, the relationships among displacement, velocity, and time can be described using specific kinematic equations, where velocity increases linearly with time and displacement increases quadratically.

Vector Decomposition

This entails resolving a vector into its orthogonal components, typically along the x and y axes. By utilizing trigonometric functions, any vector oriented at an angle can be broken down into individual components, a crucial process in analyzing motion in multiple dimensions.

Kinematic Equations

These are mathematical formulas that relate the parameters of motion—displacement, initial velocity, final velocity, acceleration, and time—in scenarios of constant acceleration. They provide the framework to predict future states of moving objects when initial conditions and acceleration are known.

Initial Conditions in Kinematics

This concept refers to the starting values of position and velocity which serve as the basis for solving kinematic problems. Accurate use of these initial values is essential to correctly applying kinematic equations to calculate subsequent motion.

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