4. 2D Kinematics

Intro to Motion in 2D:Position & Displacement

Intro to Motion in 2D: Position & Displacement

2D Position

The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s2)t2]î + (0.0190 m/s3)t3ĵ. (b) At t = 5.00 s, how far is the squirrel from its initial position?

A particle's trajectory is described by x = (1/2t^2 - 2t^2)m and y = (1/2 t^2-2t)m, where t is in s. (a) What are the particle's position and speed at t = 0 s and t = 4s?

CALC A 100 g bead slides along a frictionless wire with the parabolic shape y = (2m⁻¹) x^2. a. Find an expression for aᵧ, the vertical component of acceleration, in terms of x, vₓ, and aₓ.
Hint: Use the basic definitions of velocity and acceleration.

Displacement in 2-D

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt2, where α = 2.4 m/s and β = 1.2 m/s2. (a) Sketch the path of the bird between t = 0 and t = 2.0 s.

<p>At point A, a hiker is 10m east from the origin. After 35s, the hiker arrives at point B 40m at 60° north of east from the origin. Calculate the magnitude and direction of the hiker’s displacement.</p>

Final Position Vector

A particle moving in the xy-plane has velocity v = (2ti + (3-t^2)j) m/s, where t is in s. What is the particle's acceleration vector at t = 4s?

Scientists design a new particle accelerator in which protons (mass 1.7 X 10^-27 kg) follow a circular trajectory given by r = c cos (kt^2) î + c sin (kt^2) ĵ, where c = 5.0 m and k = 8.0 x 10^4 rad/s^2 are constants and t is the elapsed time. a. What is the radius of the circle?

There is not enough information to answer this question.

Three footballs are punted into the air at <math display="inline"><mrow><mn>32</mn><mo rspace="thickmathspace">&#x2062;</mo><mrow><mi mathvariant="normal" class="MathML-Unit">m</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">s</mi></mrow></mrow></math>. Ball A has a launch angle of 34°, Ball B has a launch angle of 41°, Ball C has a launch angle of 57°. Which ball has the longest hang time?  In other words, which ball is in the air for the longest time?

2D Displacement

Two-Dimensional Motion and Displacement | Physics with Professor Matt Anderson | M4-01

Anderson Video - 2D Motion and Displacement

Intro to Motion in 2D

Position and Displacement in 2D

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