4. 2D Kinematics
Intro to Motion in 2D: Position & Displacement Practice Problems
4. 2D Kinematics
Intro to Motion in 2D: Position & Displacement Practice Problems
6 problems
Suppose that the particle's position depends on time and it moves according to the equation x = (1/3t3 - t2)m and y = (1/4 t2-t)m. Determine where the particle is at (i) t = 0 s and (ii) t = 6 s. Also, find its speed at the given time intervals.
Any vector in a two-dimensional coordinate system can be reduced into its components (x and y). At t = 8s, what should the particle's acceleration vector be if its velocity is v = (4tî + (5-t2)ĵ) m/s?
A private tech company built one of the most advanced and powerful particle accelerators ever. The accelerator uses electricity to 'push' the charged particles (electrons) along a circular path, making them go faster and faster. The path they follow is given by the equation r = v cos (kt2) î + v sin (kt2) ĵ, where v = 4 m and k = 7 x 104 rad/s2 are constants and t is the time. Determine the circle's radius.
Consider a projectile's (m = 150 g) parabolic trajectory given by the equation y = (4m⁻¹) x2. Using the standard definitions of velocity and acceleration, find an expression that expresses ay, the acceleration's vertical component, in terms of x, vx, and ax.
In the jungle, the position of the monkey in the yz-plane is given by the coordinates
y(t) = At - 0.4 m
z(t) = Bt2 m
where A = 1.1 m/s and B = 0.95 m/s2.
Sketch the path that the monkey takes for 10 seconds from its initial position.
The position of a hypothetical quark moving in sub-atomic space is given by
Calculate how far the hypothetical quark is from its initial position after a period of 4 seconds. The unit of the function s is in angstroms (10-10 m) and the time t is in seconds.
