U(x) = U, e-x/a A particle of mass m moves in the one-dimensional potential x2 U(x) = U,
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Derive the expression for the time period of the motion when |x| ≪a.


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- An object located at ?⃗0 = (1, 1) ? is displaced by Δ?⃗01 = −2?̂ − 5?̂ ? The object is then displaced by Δ?⃗12 = 3?̂ + 2?̂ ? a) Draw a picture b) What is the final position (?⃗2) of the object? c) How far did the object travel during each displacement? (?: 5.39 ?; 3.61 ?) d) What is the total distance travelled by the object? (?: 9 ?) e) How far did the object end up from where it initially started?(?: 3.16?)Consider the motion described by the figure below. (a) Find the displacement at t = 12.4 s(b) Find the displacement at t = 12.9 s(c) Find the displacement at t = 16.5 s16
- ● S/2 | sin(t) |dt •(3+27) de dx - (18) The acceleration function in km/sec² is a(t) 3t+7 where time t is in seconds, and 0 ≤t≤ 10. Let v(t) (in km/sec) and s(t) (in km) be the velocity and position functions = 4 km. = 45 km/sec and the initial position s(0) respectively with the initial velocity, v(0) Find the velocity function and the position functions. Then, find the total distance covered.The function s(t) describes the motion of a particle along a line s(t)= t^2_18t+24 a) identify the time intervals in which the particles is moving in a negative directionThe magnitude of a particle's velocity is observed to vary with time according to the equation: |v = Bt where Bis a positive constant. What are the units of B? т S m Om: s? O m· .3 m
- PLEASE ANSWER QUICKLT AND WILL RATE HIGHLY *15Problem 3: Continue drawing the motion diagram below of an object in steady (constant velocity) traveling in the horizontal axis every 1 second, indicating the velocity vectors along the motion. t = 0 sec V t = 1 sec Problem 4: Continue drawing the motion diagram below of an object in a free-fall motion every 1 second, indicating the velocity vectors along the motion. v = 0 m/s V t = 0 sec t = 1 secA particle moves along the x-axis with position function x(t) = At² + B²²³, where 4 = 3 m s-² and B=ms-3 are constants. Find the instantaneous velocity vx and the instantaneous acceleration ax of the particle at time t = 2 s. Give your answers by entering the appropriate integer numbers in the two empty boxes below (you don't need to concern yourself with significant figures in this question). At time t=2s : Vx = At time t=2s : ax = ms-1. ms-2. You may use the following standard derivative: dc4" dt nCtn - 1 where C and are any constants. n