Suppose the initial position of an object is zero, the starting velocity is 3 m/s and the final velocity was 10 m/s. The object
moves with constant acceleration. Which part of a velocity vs. time graph can be used to calculate the displacement of the object? A. the area of the rectangle under the line B. the area of the rectangle above the line C. the area of the rectangle plus the area of the triangle under the line D. the area of the rectangle plus the area of the triangle above the line
2 answers:
Answer:
C. the area of the rectangle plus the area of the triangle under the line
Explanation:
Based on the information provided, the velocity vs. time graph is a line with a positive slope and a y-intercept of (0, 3). The displacement is the area under this line. This area can be divided into a triangle and a rectangle. So of the options available, C is the correct one.
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Explanation:
A) To prove the motion of the center of mass of the cylinders is simple harmonic:
System diagram for given situation is shown in attached Fig. 1
We can prove the motion of the center of mass of the cylinders is simple harmonic if
where aₓ is acceleration when attached cylinders move in horizontal direction:
<h3>PROOF:</h3>rotational inertia for cylinders is given as:
-----(1)
Newton's second law for angular motion is:
∑τ = Iα ------(2)
For linear motion in horizontal direction it is:
∑Fₓ = Maₓ ------ (3)
By definition of torque:
τ = RF --------(4)
Put (4) and (1) in (2)
from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate
So above equation becomes
------ (5)
As angular acceleration is related to linear by:
Eq (5) becomes
---- (6)
aₓ shows displacement in horizontal direction
From (3)
∑Fₓ = Maₓ
Fₓ is sum of fs and restoring force that spring exerts:
----(7)
Put (7) in (3)
[/tex] -----(8)
Using (6) in (8)
--- (9)
For spring mass system
----- (10)
Equating (9) and (10)
then (9) becomes
(The minus sign says that x and aₓ have opposite directions as shown in fig 3)
This proves that the motion of the center of mass of the cylinders is simple harmonic.
<h3 /><h3>B) Time Period</h3>Time period is related to angular frequency as:
