The cycle ends at time: Time ( 3.5 0.5 1 1.5 2.5 3. 3.5 1.5 25 N. Displacement XC
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- 8. The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin ët + 3 cos mt, where t is measured in seconds. (a) Find the average velocity during each time period: (i) [1, 2] (iii) [1, 1.01] (ii) [1, 1.1] (iv) [1, 1.001]11.33What is her displacement from 0 - 14 s
- 3. The position of a pinewood derby car was observed at various times; the results are summarized in the following table. Find the average velocity of the car for (a) the first second, Answer (b) the last 3 s, and Answer (c) the entire period of observation. t (s) 1.0 2.0 3.0 4.0 5.0 æ (m) 2.3 9.2 20.7 36.8 57.52. a. A particle is undergoing a uniform rectilinear motion and the displacement as a function of time is given by r(t) = 6tª- 2t³ -12t²+3t+3 where r is in meters and t is in seconds. b. What is a uniform rectilinear motion? c. Find the average acceleration of the particle between t = 0 and t = 2s d. When is the acceleration zero? = 3. The position of a particular particle as a function of time is given by r 9.60t i+ 8.58 j - 1.00t² k) m. Determine the particle's velocity and acceleration as a function of time.Given the plot of distance versus time below. At which time is the object not moving? 20 15 10 1 2 3 4 5 6 time (s) distance (m) 55 0 0 A. 1.5 s B. 2.5 s OC. 3.5 s D. 4.5 s E. B and D
- 10.1 A VPN KB/s 79 46. 46 4:04 O O A particle moves along an x axis from point A to point B with average velocity v1 = 4.00 m/s through displacement Ax1= 20.0 m. Then it moves at average velocity v2 through displacement Ax2 = 30.0 m from point B to point C. If the total time is 7.00 s, what is the value of v2? A Number i Units ()A weight is oscillating up and down on spring. It's displacement from rest is given by the function d(t)=sin6t-4cos6t, where d is in centimetres and t is time in seconds. a. what is the rate of change of the displacement after 1s b. Determine the maximum and minimum displacements and when they first occur.Question 4 A stretched string of length 50 cm is plucked a quarter of the way along its length to give an initial velocity of 10 m/s. Find expressions for the coefficients an and bn. a. an = 0 bn = 0 -0.5 b. an = 0.25 y(x,0) sin(kx)dx, b₁ = 0 4 0.5 = c. an = 0, bn foy(x,0) sin(kx) dx @n 4 -0.5 d. an = So y(x,0) sin(kx) dx, y(x,0)sin(kx)dx Wn b₁ =0.255 0
- 3 1 3 4 5 t (s) What is the particle's acceleration at t = 4.5 s? 1 m/s^2 -1 m/s^2 -2 m/s^2 3 m/s^2 O 2 m/s^2 (s/w) AA particle moves along the x-axis according to r(t) = 20t - 4t² m. Help on how to format answers: units. a. Determine the instantaneous velocity at each of the following times. At time t = 1s the instantaneous velocity is: At time t = 8s the instantaneous velocity is: b. Determine the instantaneous speed at each of these times. At time t = 1s the instantaneous speed is: At time t = 8s the instantaneous speed is: c. What is the average velocity between t = 1s and t = 8 s? Answer:The position, x in meter (m) of an object that move a straight line as a following relation X= 16 -12t + 4t? +4 Find: a. The average velocity at time t=0, t= 2 sec b. The average acceleration at time t=0, t=2 sec c. The instantaneous velocity and instantaneous acceleration at time t=0, t = 2 sec, t= 4sec,t=6sec