An acceleration vs. time graph for an object moving along a line is shown. The value of T = 8.0 s and the value of A = 11.0 m/s2. The object is moving at v = 0.8 m/s at time t=0 s from initial position x = -1.34 m. The graph shown is sinusoidal (meaning it can be written as a sine function or a cosine function) and assumed to continue for all time. (A) Please determine the acceleration as a function of time for the object. (B) Please determine the velocity as a function of time for the object (C) Please determine the position as a function of time for the object
An acceleration vs. time graph for an object moving along a line is shown. The value of T = 8.0 s and the value of A = 11.0 m/s2.
The object is moving at v = 0.8 m/s at time t=0 s from initial position x = -1.34 m. The graph shown is sinusoidal (meaning it can be written as a sine function or a cosine function) and assumed to continue for all time.
(A) Please determine the acceleration as a function of time for the object.
(B) Please determine the velocity as a function of time for the object
(C) Please determine the position as a function of time for the object
![2T
Time (s)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a58d27d-7bef-4574-b92f-c82cded2551c%2F48f1e48e-43d9-4fb3-8a6c-b713ed687911%2F735k2in_processed.png&w=3840&q=75)
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Given
- The amplitude of the graph or maximum acceleration is .
- The time period of the graph is .
- The initial velocity of an object is .
- The initial position of an object is .
The angular frequency is calculated as,
The graph is shown the sine wave. The acceleration of the object is calculated as,
Substitute t=0 and a=0,
Therefore the acceleration is calculated as,
Thus, the acceleration as a function of time for the object is.
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