Question

1. what is the velocity of a particle that travels from 0 to 65 feet, in 12 seconds? (answer in fps)?
2. what is the acceleration of the same particle if its velocity was to change to 25 fps in 2 seconds? (use particle equations ( v = \frac{x_2 - x_1}{t_2 - t_1} ) and ( a = \frac{delta v}{delta t} ))
3. what are 2-3 advantages of solid metal piping in hydraulic systems?
4. what are 2-3 advantages of flexible hose/tubing in hydraulic systems?

Explanation:

Question 1

Step1: Identify values for velocity formula

The formula for velocity \( v \) is \( v=\frac{x_2 - x_1}{t_2 - t_1} \). Here, \( x_1 = 0 \) feet, \( x_2 = 65 \) feet, \( t_1 = 0 \) seconds, \( t_2 = 12 \) seconds.

Step2: Substitute values into the formula

Substitute the values into \( v=\frac{x_2 - x_1}{t_2 - t_1} \), we get \( v=\frac{65 - 0}{12 - 0}=\frac{65}{12}\approx5.42 \) (fps).

Step1: Identify values for acceleration formula

The formula for acceleration \( a \) is \( a=\frac{\Delta v}{\Delta t} \). Here, \( \Delta v = 25 \) fps (change in velocity), \( \Delta t = 2 \) seconds (time interval).

Step2: Substitute values into the formula

Substitute the values into \( a=\frac{\Delta v}{\Delta t} \), we get \( a=\frac{25}{2} = 12.5 \) (fps²).

1. Durability: Solid metal piping is highly durable and can withstand high pressure, temperature, and mechanical stress in hydraulic systems, reducing the risk of leaks or bursts.
2. Resistance to Corrosion: Many metal pipes (like stainless steel or galvanized steel) have good corrosion resistance, which is crucial in hydraulic systems where fluid - metal interaction can cause corrosion over time.
3. Long - term Cost - effectiveness: Although the initial cost may be higher, solid metal piping has a long lifespan, reducing the need for frequent replacements and maintenance, thus being cost - effective in the long run.

Answer:

The velocity of the particle is approximately \(\frac{65}{12}\) or \( 5.42 \) fps.

Question 2