Ball rolling up an incline Final Exam Review

charan1

1. The problem statement, all variables and given/known data
A ball rolls up a straight incline. The dots in the diagram represent the position of the ball every 4 seconds.
(The fourth dot is not intended to represent the turnaround point; the ball might still be on the way up at that
point.) The instantaneous velocities at the second and third dots are as given in the diagram.

a. Determine the velocities at the locations of the first and fourth dots and label them on the diagram. (2 points)

b. Determine how far the ball travels between the second and third dots. (3 points)

(IMAGE attached!)


2. Relevant equations

a_avg= Delta V/ Delta T

3. The attempt at a solution
I am kind of stumped at this problem and not sure where to begin or how to get where I'm trying to go, all I could think to do was this...then I wasn't sure where to go from there.

(5m/s² + 7m/s²) / 2 = Delta V/(8s-4s)

Delta V = 24m/s

Please help! thank you

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charan1

woops! those are not accelerations they are velocities! sorry I will return when I attempt to figure it out again!

charan1

also adding to the question

Part C:
Determine the total time it takes the ball to roll up the incline, from the bottom to the turnaround point.

charan1

Part A:
Equations:
Vf=Vi+a(delta T)
a_avg=D=(delta V)/(delta T)

V_{Dot 2}=7m/s
V_{Dot 3}=5m/s

a_avg=(5m/s-7m/s)/(8s-4s)=-.5m/s²

V_{Dot 2}=V_{Dot 1}+(-.5m/s/s)(4s-0s)
V_{Dot 1}=9m/s

V_{Dot 4}=V_{Dot 3}+(-.5m/s/s)(12s-8s)
V_{Dot 4}=3m/s

Part B:

Equation:
vf²=vi²+2a(delta x)

5²=7²+2(-.5m/s/s)(delta x)
(Delta x)=24m

Part C:

Equation:
vf=vi+a(delta T)

vf=0m/s
vi=9m/s
a=-.5m/s/s
(delta T)=?

0m/s=(9m/s)+(-.5m/s/s)(delta T)

(delta T)=18s

Please check thank you!