Ch 03: 2D Motion (Projectile Motion)See all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Intro to 2D Motion

See all sections
Sections
Intro to 2D Motion
Projectile Motion
More Projectile Motion
Initial Velocity in Projectile Motion
Circular Motion

Solution: The velocity vector v(t) measured in m/s for a particle at time t is given as  v(t) = [(3t + 4t3)î − 2ĵ] m/s, where t is in seconds. [a] Find the units of the coefficients 3, 4, and 2 in the vector  v. [b] Find the average acceleration in the interval t = 0 to t = 2 seconds. [c] Find the acceleration at t = 2 s. [d] Say that at t = 0 the particle is at the origin, r(0) = 0. Find the position vector  r(t). [e] Eliminate t to give the equation of the trajectory x as a function of y.

Problem

The velocity vector v(t) measured in m/s for a particle at time t is given as  v(t) = [(3t + 4t3)î − 2ĵ] m/s, where t is in seconds.

[a] Find the units of the coefficients 3, 4, and 2 in the vector  v.

[b] Find the average acceleration in the interval t = 0 to t = 2 seconds.

[c] Find the acceleration at t = 2 s.

[d] Say that at t = 0 the particle is at the origin, r(0) = 0. Find the position vector  r(t).

[e] Eliminate t to give the equation of the trajectory x as a function of y.