Answer:
The magnitude of the force is 64.634 newtons.
Explanation:
According to the statement, the crate is a constant mass system, whose upward force is described by the following expression:
(1)
Where:
- Force, in newtons.
- Mass, in kilograms.
- Acceleration, in meters per square second.
The function acceleration is obtained by deriving the function position twice in time:
(2)
(3)
And we expand (1) by applying (3):
Where 
is the time, in seconds.
If we know that 
and 
, then the magnitude of the force is:
The magnitude of the force is 64.634 newtons.
Answer:
The answer is B.
Explanation:
You're given a position vs. time graph. The the slope of the line is the change in position over time - in other words, the speed.
A positive slope indicates a positive change in position over time and therefore a positive speed. The more positive the slope, the greater the change and the greater the positive speed.
A negative slope indicates a negative change in position over time and therefore a negative speed. The more negative the slop, the greater the change and the greater the negative speed.
A horizontal slope (i.e. slope of 0) indicates no change in position over time. In other words, the speed is 0 and the object is stationary.
With this in mind, you can see the object is initially moving with a positive speed for 3 s (from t=0 to t=3), then is at rest for 3 s (from t=3 to t=6), then is moving at a (higher) positive speed for 4 s (from t=6 to t=10). You can see then that the answer is B.
A is wrong because after being at rest the object moves at a constant speed for only 4 s.
C is wrong because by the time the object gets to 5cm, it has moved at 3 different speeds (first positive slope, horizontal slope, second positive slope).
D is wrong because the object moves from 0 to 3cm in 3 s - a speed of 3cm/3s = 1cm/s.
