Kinematics problem -- A particle is moving with changing acceleration....

In summary, the question provided from the reference book for Exercise 16.2, Q7 is nonsensical and does not have a clear solution. There are multiple possible interpretations of the problem, but none of them result in the given answer of t=3.06s.
  • #1
daisybeh
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Poster warned about not providing an attempt at a solution
Homework Statement
please help on kinematics problem
Relevant Equations
v=ds/dt, a=dv/dt
A particle, P, starts from rest at a point X and moves in a straight line with an acceleration expressed as a=4t. After 2 seconds, the particle reaches Y and it stops accelerating. The particle leaves Y with a velocity -3ms-1, and finally comes to rest at Z.
(i) Find the value of t when the particle reaches Z. (answer is t=3.06s)
 
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  • #2
daisybeh said:
Problem Statement: please help on kinematics problem
Relevant Equations: v=ds/dt, a=dv/dt

A particle, P, starts from rest at a point X and moves in a straight line with an acceleration expressed as a=4t. After 2 seconds, the particle reaches Y and it stops accelerating. The particle leaves Y with a velocity -3ms-1, and finally comes to rest at Z.
(i) Find the value of t when the particle reaches Z. (answer is t=3.06s)

That problem doesn't make sense to me. Are you sure you've written it correctly?

As with your other post, you need to show us how much of this you can do.
 
  • #3
PeroK said:
That problem doesn't make sense to me. Are you sure you've written it correctly?

As with your other post, you need to show us how much of this you can do.
I got this question from my reference book. I can't get the answer.
 
  • #4
daisybeh said:
I got this question from my reference book. I can't get the answer.

This is not a forum where we do your homework for you. Our approach is to help you where you get stuck. This involves you doing as much of the problem as possible, so we can see where you are going wrong.

In this case, however, the problem is clearly nonsensical. If that's what your book really says, then I'd skip this problem.
 
  • #7
A particle, P, starts from rest at a point X and moves in a straight line with an acceleration expressed as a=4t.
Assuming "t" here is the time, in seconds, after the particle started moving (which should have been explicitly said) then its speed after t seconds is [tex]2t^2[/tex] and it will have traveled a distance of [tex]\frac{2}{3}t^3[/tex].

After 2 seconds, the particle reaches Y and it stops accelerating.
Taking X to be 0, [tex]Y= \frac{2}{3}2^3= \frac{16}{3}[/tex] and the particle's speed at Y is 2(4)= 8.

The particle leaves Y with a velocity -3ms-1, and finally comes to rest at Z.
This is the part that makes no sense! If the particle has the constant velocity [tex]-3 m/s[/tex] then it will never come to rest!

If, instead, the particle left Y with acceleration [tex]-3 m/s^2[/tex] then its velocity t seconds after leaving Y is [tex]\frac{16}{3}- 3t[/tex] which will be 0 when [tex]t= \frac{16}{9}[/tex]. That is not "3.06" so apparently that is not a correct interpretation either!

Another possibility is that something happened at Y so that the velocity dropped instantaneously from 8 to -3 m/s while there was still the acceleration 4t. Then the speed t seconds after leaving Y is [tex]-3+ 2t^2[/tex]. The particle will stop when [tex]-3+ 2t^2= 0[/tex] so [tex]t= \sqrt{\frac{3}{2}}[/tex]. No, that's not "3.06" either! I am baffled by this problem.
 
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FAQ: Kinematics problem -- A particle is moving with changing acceleration....

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It involves concepts such as position, velocity, acceleration, and time.

2. What is a particle in kinematics?

In kinematics, a particle is a term used to describe a point object with mass that is moving in space. It is a simplification of an object's motion, assuming it has no size or shape and all its mass is concentrated at a single point.

3. How do you solve a kinematics problem?

To solve a kinematics problem, you need to identify the given information, such as initial and final positions, velocities, accelerations, and time. Then, you can use equations of motion, such as the kinematic equations, to calculate the unknown variables.

4. What is changing acceleration in kinematics?

Changing acceleration, also known as variable acceleration, refers to the scenario where an object's acceleration is not constant but changes over time. This can happen when there is a change in the object's speed or direction, or when external forces act on the object.

5. How does kinematics relate to other branches of physics?

Kinematics is closely related to other branches of physics, such as dynamics and mechanics. Dynamics deals with the forces that cause motion, while kinematics focuses on the motion itself. Mechanics, on the other hand, combines both kinematics and dynamics to study the motion of objects under the influence of forces.

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