When vibrational motion in an object increases, which is a true statement?
1 answer:
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A) Acceleration:
B) The total displacement is 209.5 m north
C) The average velocity is 8.06 m/s north
Explanation:
A)
Acceleration is defined as:
where
v is the final velocity
u is the initial velocity
t is the time taken for the velocity to change from u to v
Here we have:
- In the first segment,
u = 8 m/s north
v = 11 m/s north
t = 4 s
So the acceleration is
(north)
- In the second segment, Stan drives at a constant velocity: so the final velocity is equal to the initial velocity,
u = v
Therefore, the acceleration is zero:
- In the third segment,
u = 11 m/s (north)
v = 0 (he comes to a stop)
t = 7 s
So the acceleration is
And the negative sign means the acceleration is south, opposite to the direction of motion.
B)
In a uniformly accelerated motion, the displacement can be calculated as:
where
u is the initial velocity
a is the acceleration
t is the time
- For the first segment, we have
So the displacement is
- For the second segment, we have
So the displacement is
- For the third segment, we have
So the displacement is
So the total displacement is:
s = 6 m + 165 m + 38.5 m = 209.5 m
In the north direction (positive direction)
C)
The average velocity is given by:
where
d is the total displacement
t is the total time
Here we have:
d = 209.5 m
t = 26 s
Therefore, the average velocity is
(north)
Learn more about accelerated motion:
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