Kinetmatics of rectilinear motion

In summary, the question is asking for the acceleration of a point P that starts from rest and accelerates uniformly to a speed of 88 ft/sec after traveling 120 ft. The solution involves integrating the velocity with respect to time and the acceleration with respect to distance, which can be confusing. The standard kinematics equations may provide a simpler solution.
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Homework Statement



A point P starts from rest and accelerates uniformly (meaning x'' = constant) to a speed of 88 ft/sec after traveling 120 ft. Find the acceleration of P.

Homework Equations



x=position
v=velocity=dx/dt
a=acceleration=dv/dt


The Attempt at a Solution



The answer is 32 ft/s^2. Please look at the attachment for the solution. I don't understand it. Why is v integrated with respect to dv while the acceleration x'' is integrated with respect to t? Also wouldn't the integral of v give the position while the integral of acceleration give the velocity? How are they then equal? Sorry but I'm confused about this. Any help appreciated thanks!
 

Attachments

  • equation answer.gif
    equation answer.gif
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  • #2
The attachment does not appear to be any sort of solution.

Why not use the standard kinematics equations?
 

Related to Kinetmatics of rectilinear motion

1. What is kinematics of rectilinear motion?

Kinematics of rectilinear motion is the study of the motion of objects in a straight line, without considering the forces that cause the motion.

2. What are the basic equations used in kinematics of rectilinear motion?

The three basic equations used in kinematics of rectilinear motion are:

  • Position (x) = Initial position (x0) + Initial velocity (v0) x Time (t) + 1/2 x Acceleration (a) x Time (t)^2
  • Final velocity (v) = Initial velocity (v0) + Acceleration (a) x Time (t)
  • Final position (x) = Initial position (x0) + Average velocity (vavg) x Time (t)

3. How is displacement different from distance in kinematics of rectilinear motion?

Displacement refers to the change in position of an object in a straight line, while distance refers to the total length traveled by the object, regardless of direction. Displacement is a vector quantity, while distance is a scalar quantity.

4. How is acceleration calculated in kinematics of rectilinear motion?

Acceleration is calculated by dividing the change in velocity by the change in time. The equation for acceleration is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

5. What is the difference between average velocity and instantaneous velocity in kinematics of rectilinear motion?

Average velocity is the total displacement divided by the total time, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity can be calculated using the equation vavg = (xf - xi) / t, where xf is the final position, xi is the initial position, and t is the time interval.

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