Difficulty with a basic motion problem

  • Thread starter Thread starter frankfjf
  • Start date Start date
  • Tags Tags
    Difficulty Motion
AI Thread Summary
To solve the motion problem defined by the position function x = 2.30t^5, the average velocity between t = 1.0 s and t = 2.0 s can be calculated using the formula for average velocity, which is (x(t_b) - x(t_a)) / (t_b - t_a). The average acceleration is similarly derived from the change in velocity over the time interval. For instantaneous values, the velocity is found by taking the derivative of the position function, while the acceleration is the derivative of the velocity function. Clarification on calculating the two velocities for average acceleration is provided, emphasizing the need for derivatives of the position function.
frankfjf
Messages
166
Reaction score
0
This time I'm having trouble with this problem:

If the position of an object is given by x = 2.30t^5, where x is measured in meters and t in seconds, find (a) the average velocity and (b) the average acceleration between t = 1.0 s and t = 2.0 s. Then find (c) the instantaneous velocity v and (d) the instantaneous acceleration a at t = 1.0 s. Next find (e) v and (f) a at t = 2.0 s.

I have solved a, but am uncertain how to obtain the two velocities needed for b according to the formula for average velocity. What do I need to do?
 
Physics news on Phys.org
the velocity function is the time-derivitive of the location function.

the acceleration function is the time-derivitive of the velocity function.
 
the average velocity forumula is [f(b)-f(a)]/b-a, the avg. acceleration formula is essentially the same except that for the values of f(b) and f(a) you need to take the derrivative of the position equation to give the velocity values
 
aud11888 means that average velocity = \frac{x(t_b) - x(t_a)} {t_b - t_a}
 
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 .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top