8.6. Examples and Problem Solving

Try these first

1. 1.

   What is Newton's second law?

   Hint

   Think about how mass and acceleration are related to force.

2. 2.

   Define acceleration in terms of velocity.

   Hint

   Consider how fast the velocity is changing.

3. 3.

   What does Newton's second law state?

   • Acceleration equals mass times force
   • Force equals mass times acceleration
   • Mass equals force times acceleration

   Hint

   Refer to the formula F = ma.

4. 4.

   Local acceleration is dependent on:

   • True
   • False

   Hint

   Consider if time affects acceleration at points.

5. 5.

   A fluid has a velocity field represented as V = (2x, 3y, -y). Calculate the material accelerations at the point (1, 2, 1).

   Hint

   Consider looking at spatial derivatives to derive acceleration components.

6. 6.

   Given a velocity function V(x,t) = 5x^2 + t and the density of fluid ρ(y) = 2y, find the material derivative of velocity.

   Hint

   Use partial derivatives as you connect variables to their respective equations.