a) 120 s
b) v = 0.052R [m/s]
Explanation:
a)
The period of a revolution in a simple harmonic motion is the time taken for the object in motion to complete one cycle (in this case, the time taken to complete one revolution).
The graph of the problem is missing, find it in attachment.
To find the period of revolution of the book, we have to find the time between two consecutive points of the graph that have exactly the same shape, which correspond to two points in which the book is located at the same position.
The first point we take is t = 0, when the position of the book is x = 0.
Then, the next point with same shape is at t = 120 s, where the book returns at x = 0 m.
Therefore, the period is
T = 120 s - 0 s = 120 s
b)
The tangential speed of the book is given by the ratio between the distance covered during one revolution, which is the perimeter of the wheel, and the time taken, which is the period.
The perimeter of the wheel is:

where R is the radius of the wheel.
The period of revolution is:

Therefore, the tangential speed of the book is:

Answer:
Explanation:
Given the velocity of a particle modeled by the equation
v = 13-3t+8t² where t is in seconds
Given t = 0 and position s = +5m
A) To get the position as a function of time, we will integrate the function with respect to t ad shown;
v = 13-3t+8t²
S = ∫13-3t+8t² dt
S = 13t-13t²/2+8t³/3 + C
at t = 0 and S = +5m
5 = 13(0)-13(0)²/2+8(0)³/3+C
5 = 0-0+0+C
C = 5
Substituting c = 5 into the displacement function
S = 13t-13t²/2+8t³/3 + C
S = 13t-13t²/2+8t³/3 + 5
B) acceleration is the change in velocity with respect to time.
a = dv/dt
Given v = 13-3t+8t²
a= dv/dt = -3+16t
a = 16-3t
C) acceleration at t = 6s is derived by plugging in t = 6 into the resulting equations in (B)
a = 16-3t
a = 16-3(6)
a = 16-18
a = -2m/s²
D) net displacement from t = 0 to t = 6s
At t = 0:
S(0) = 13(0)-13(0)²/2+8(0)³/3 + 5
S(0) = 0+5
S(0) = 5m
At t = 6s
S(6) = 13(6)-13(6)²/2+8(6)³/3 + 5
S(6) = 78-234+576+5
S(6) = 425m
Net displacement from t = 0s to t = 6s is s(6)-s(0)
= 425-5
= 420m
E) Total distance travelled D = S(6)+S(0)
= 425+5
= 430m
F) Average velocity = ∆S/∆t
Average velocity = S(6)-S(0)/6-0
Average velocity = 425-5/6
Average velocity = 420/6
Average velocity = 70m/s
Answer:
The formula to calculate velocity in this case:
v = v0 + at
=> a = (v - v0)/t
= (50 - 0)/4
= 50/4 = 12.5 (m/s2)
Hope this helps!
:)
Answer:
V = 2.5 J/C
Explanation:
<u><em>Given:</em></u>
Energy = E = 20 J
Charge = Q = 8 C
<u><em>Required:</em></u>
Potential Difference = V = ?
<u><em>Formula:</em></u>
V = 
<u><em>Solution:</em></u>
V = 20/8
V = 2.5 J/C