No problem, glad I could help!

In summary, Kinematics is a branch of classical mechanics that focuses on the motion of objects without considering the forces behind it. This involves studying the position, velocity, and acceleration of objects in space and time. In Kinematics, a vector is a quantity that has both magnitude and direction, while a scalar only has magnitude. The Vector DE Equation in Kinematics represents the relationship between an object's position, velocity, and acceleration. Kinematics has real-life applications in sports, amusement park rides, traffic, engineering, robotics, and animation.
  • #1
FeDeX_LaTeX
Gold Member
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Kinematics -- Vector DE

Homework Statement


f516dt.jpg


The Attempt at a Solution


Here's their solution.

5wca2r.jpg


I'm stuck on (b). The first and second lines are fine. But how do they get from the second line to the third line? And then in the fourth line, why are they integrating from u^2 to v^2?

EDIT: Sorry for the image size.
 
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  • #2
They make the substitution v2 = x.

Chet
 
  • #3
Chestermiller said:
They make the substitution v2 = x.

Chet

That's it?! I thought x denoted position (as a function of time)! Was losing my mind over this. Thanks.
 

Related to No problem, glad I could help!

What is Kinematics?

Kinematics is a branch of classical mechanics that deals with the motion of objects without considering the forces that cause the motion. It involves studying the position, velocity, and acceleration of objects as they move through space and time.

What is a Vector in Kinematics?

In Kinematics, a vector is a quantity that has both magnitude and direction. In other words, it is a mathematical representation of a physical quantity that has a size and a direction, such as velocity or acceleration.

What is the difference between Scalar and Vector in Kinematics?

The main difference between scalar and vector quantities in Kinematics is that scalar quantities only have magnitude, while vector quantities have both magnitude and direction. Examples of scalar quantities include distance, speed, and time, while examples of vector quantities include displacement, velocity, and acceleration.

What is the Vector DE Equation in Kinematics?

The Vector DE Equation in Kinematics is a mathematical representation of the relationship between an object's position, velocity, and acceleration. It is written as dE/dt = v = d/dt(x), where dE/dt represents the rate of change of an object's position, v represents the velocity, and d/dt(x) represents the derivative of an object's position with respect to time.

How is Kinematics used in real life?

Kinematics has many practical applications in real life, including predicting the motion of objects in sports, designing roller coasters and other amusement park rides, and understanding the movements of vehicles in traffic. It is also used in engineering, robotics, and animation to simulate and control the motion of machines and characters.

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