Answer is E.
Since
at t=0=>x(t) =0
Therefore
N3T.4 If a car's x-position at time t-0 is x(0) it has an r-velocity of v(t)...
4. A car's position as a function of time is given by the following equation: x(t)-5 m/s t+2.8 m/s2 t-0.15 m/s3 t3. a. Find the average velocity from 0 to 5 s b. Find the instantaneous velocity at 0, 3, and 5s. c. Find the average acceleration from 0 to 5 s. d. Find the instantaneous acceleration at 0, 3, and 5 s. e. At what POSITIVE time does the car come to rest?
Find the velocity r and the position a as functions of the time t for a particle of mass m, which starts from rest at -0 and t 0, subject to the force F Fo br. Find the potential energy function U(x) for this force.
Suppose that, at time t = 0, a particle with mass 3 has position vector ⃗r(0) = 4⃗j − ⃗k and velocity ⃗v(0) = −5⃗j − 13⃗k. The particle is then subjected to a constant force of F⃗ = 9⃗ı + 6⃗k. (a) Find the position of the particle (as a function of time). (b) When is the particle moving most slowly? Compare the minimum speed with the speed at times t = 1 and t = 4. Thank you!...
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
(a) At time t 0, a one-dimensional bound system is in a state described by the normalized wave function V(r,0). The system has a set of orthonormal energy eigenfunctions (), 2(x),.. with corresponding eigenvalues E, E2, .... Write down the overlap rule for the probability of getting the energy E when the energy is measured at time t 0 (b) Suppose that a system is described by a normalized wave function of the form (,0) an(r), where the an are...
Consider an object moving along a line with the following velocity and initial position. v(t) = 9 -12 on [0, 4); $(0) = -1 Determine the position function for t20 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the two methods. To determine the position function for t20 using the antiderivative method, first determine how the velocity function and the position function are related. Choose the correct answer below. O A. The position...
ection 2.2 4. An electron moving along the x axis has a position given by x = Ate-t/r where A and are constants. Givens: A = 16 m/s. T = 1.0s. (a) Sketch a graph of r(t) from Os to 10s. Feel free to use a graphing calculator or other software to visualize the function. (b) Derive a symbolic expression for u(A, T, t) for the electron's instantaneous velocity as a function of time. (c) Sketch a graph of u(t)...
Suppose the position vector for a particle is given as a function of time by r(t)-x(t)¡ + y(t), with x(t)-at + b and yte cd, where a 1.50 m/s, b - 1.35 m, c0.130 m/s2, and d -1.14 m. (a) Calculate the average velocity during the time interval from t = 1.90 s to t = 4.05 s. 0.097 X m/s (b) Determine the velocity at t 1.90 s. -|-1.006 | X m/s Determine the speed at t 1.90 s...
8. The position vector r of a point P is a function of the time t and r satisfies the vector differential equation d2r dr 2k (k2 n2)r g, dr2 where k and n are constants and g is a constant vector. Solve dr a and dt this differential equation given that r v when t = 0, a and v being constant vectors Show that P moves in a plane and write down the vector equation of this plane...
Mechanics. Need help with c) and d) 1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...