A and B are correct, I just need help with C, D, E. For rating please provide cl
ID: 3345748 • Letter: A
Question
A and B are correct, I just need help with C, D, E. For rating please provide clear work with answers, I want to understand.
Suppose that a particle moves according to the law of motion
s= (4t)/(t^2+5) , t >/= 0
(A) Find the velocity at time t.
v(t) =
(B) What is the velocity after 3 seconds?
Velocity after 3 seconds =
(C) Find all values of t for which the particle is at rest. (If there are no such values, enter 0. If there are more than one value, list them separated by commas.)
t=
(D) Use interval notation to indicate when the particle is moving in the positive direction. (If the particle is never moving in the positive direction, enter "{}" without the quotation marks.)
Answer =
(E) Find the total distance traveled during the first 8 seconds.
Total distance =
Explanation / Answer
S = 4t/(t^2+5)
V(t) = ds/dt = 4/(t^2 +5) -4t*2t/(t^2+5)^2
= (20-4t^2)/(t^2+5)^2
c) when aparticle at rest ... that is v(t) =0
(20-4t^2)/(t^2+5)^2 =0
(20-4t^2) = 0
t^2 = 5
t =2.23 s
d) particle is moving i positve direction if V(t) > 0
(20-4t^2)/(t^2+5)^2 > 0
(20-4t^2) > 0
t^2 < 5
0< t < 2.23
e) distnace travelled by particle in 8 s = distance in 2.23 s + distance in 5.77 s
= 4*2.23/(2.23^2+5) + 4*5.77/(5.77^2+5)
=0.894 + 0.602
=1.496 m
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