Physics Problem: Displacement, Acceleration, Velocity

AI Thread Summary
The discussion focuses on calculating the skateboarder's acceleration and the components of her motion on an inclined ramp. To determine her acceleration, the formula a = g sinθ is used, with θ being the ramp's angle. The average velocity is calculated as (vf - vi)/2, leading to the time of descent being derived from distance over velocity. For the displacement problem involving a car traveling at 5 m/s along a square, the displacement and average velocity are to be calculated for various points, with each side of the square measuring 20 m. The calculations emphasize the relationship between distance, velocity, and displacement in both scenarios.
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A skateboarder, starting from rest, rolls down a 11.0 m ramp. When she arrives at the bottom of the ramp her speed is 7.20 m/s.

(a) Determine the magnitude of her acceleration, assumed to be constant.

(b) If the ramp is inclined at 24.5° with respect to the ground, what is the component of her acceleration that is parallel to the ground?
 
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(a) Since the skateboarder is on an incline, a = g sinθ. To find the time it takes to descend, find the average velocity v = (vf - vi)/2. We know that t = distance/velocity, or in this case, 11/3.6. Using a = v/t, you can find that θ = ArcSin v/gt.

(b) If you draw a diagram of the problem you'll see that the x-component of acceleration is ax = a cos24.5
 
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Average Velocity = (vf+vi)/2 and acceleration = (vf-vi)/t please could you explain how average velocity has been expressed as vf-vi over 2
 
Displacement Problem:
A car travels at a speed of 5 m/s along a square root ABCD find its displacement and average velocity from A to B, from A to C and from A to D i.e from A to all the corners with length of one side of the square is = 20 m.
Find dispacement and average velocity:
i- from A to B
ii- form A to C
iii- from A to D
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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