Answer:
The equation of motion is 

Explanation:
Lets calculate
The weight attached to the spring is 24 pounds
Acceleration due to gravity is 
Assume x , is spring stretched length is ,4 inches
Converting the length inches into feet 
The weight (W=mg) is balanced by restoring force ks at equilibrium position
mg=kx
⇒ 
The spring constant , 
= 72
If the mass is displaced from its equilibrium position by an amount x, then the differential equation is



Auxiliary equation is, 

=
Thus , the solution is 

The mass is released from the rest x'(0) = 0
=0


Therefore ,

Since , the mass is released from the rest from 4 inches
inches
feet
feet
Therefore , the equation of motion is 
You want to draw a free body diagram of the forces on the sled in the horizontal x-direction.
If you visualize the system in an x-y coordinate plane, the force along the x-direction is the angle it makes with the x-axis multiples by the force.
The angle made with the x-axis is cosine of the angle theta.
Please see picture attached.
I think metal, steel and copper.
<h3>2
Answers:</h3>
a) Velocity is a vector quantity
e) Velocity is a speed with direction
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Explanation:
If we know the velocity of an object, then we know how fast it's going (speed) and where it's going (direction). It is a vector because the direction of the vector determines the direction, and the length of the vector (aka magnitude) determines the speed. So in a sense we've built in two facts of data into one visual.
An example of velocity: 10 miles per hour north. Here we have the speed of 10 mph and the direction north.
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Extra info:
- Choice B contradicts choice A, so we can cross choice B off the list.
- Choice C is false because speed is a scalar, or single quantity, and not a vector. As mentioned earlier, speed is a part of velocity, but they aren't the same exact thing.
- Choice D is false because the velocity does not account for net force. We don't have any force information built into the velocity.