Question

The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Use analytic methods to do each of the following: (a) Determine when the particle is moving to the right, to the left, and stopped. (b) Find the particle's displacement for the given time interval. If s(0) = 3, what is the particle's final position? (c) Find the total distance traveled by the particle. v(t) = 5 cos t, 0 ≤ t ≤ 2π

Answer 1

Answer:

a) Right 0≤p<π/2 and 3π/2<p≤2π

  left  π/2 ≤ p ≤3π/2

  stopped  p=π/2 and p=3π/2

b)  5.5cm and its final position (2π, 0)

c) 6.5cm

Step-by-step explanation:

we must find where the function becomes negative, positive and zero

(according to the graph)

the particle moves to the right where the function is positive

0≤p<π/2 and 3π/2<p≤2π , the particle moves to the left where the function is negative π/2 ≤ p ≤3π/2, and stopped p=π/2 and p=3π/2

s(t)=∫v(t)dt also s(t) = 5sin(t)

(according to the graph 2)

The displacement of the particle is 5.5 and its final position

(2π, 0)

The total displacement of the particle is 6.5