If the position of a particle is defined by s = [2 sin (π/5)t + 4] m, where t is in seconds, construct the s-t, v-t, and a-t graphs for 0 ≤ t ≤ 10s.
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- Please AsapAn 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?)External stimuli are communicated to the brain by means of electrical signals propagating along nerve cells at a speed of approximately 25 m/s. Similarly, electrical messages are sent at the same speed from the brain along nerve cells to the muscles. Reflex actions are controlled by a relatively simple nerve circuit from a muscle to the spine and back to the muscle. Estimate the reflex time for a stimulus at the knee. (Assume that the signal resulting from the stimulus must travel a distance Δs = 1 m.)
- 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 mA 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
- Needs Complete typed solution with 100 % accuracy.A particle moving along a straight line has initial velocity v(0) = 1 m/s, and acceleration a(t) = sin(I-t) + cos(t+1) (in m/s?). (a. Find the velocity at time t. (b) Find the average velocity during the time interval [I, 211]. (c) Find the distance traveled during the time interval [1, 2I].