Calculating Displacement and Velocity

The video tutorial explains how to calculate the displacement of a particle moving in the xy-plane with given velocity components. It starts by introducing the velocity vector and the initial position of the particle. The problem is to find the magnitude of the displacement and the position of the particle between t=1 and t=3. The tutorial breaks down the process into calculating the change in x and y using integration, and then uses the Pythagorean theorem to find the total displacement. The final position of the particle is also determined by adding the changes to the initial coordinates.

What is the initial position of the particle at t=1?

• (3, 4)

• (0, 0)

• (4, 3)

• (1, 3)

What is the x-component of the velocity function?

• 1/t

• t + 7

• t^4

• 1/t + 7

How do you find the displacement in the x direction?

• By adding the x-component of velocity to the initial position

• By integrating the x-component of velocity

• By differentiating the x-component of velocity

• By multiplying the x-component of velocity by time

What mathematical operation is used to find the change in x?

• Integration

• Addition

• Differentiation

• Multiplication

What is the result of integrating 1/t + 7 from t=1 to t=3?

• Natural log of 1

• Natural log of 3

• Natural log of 2

• Natural log of 1.25

What is the y-component of the velocity function?

• t^3

• 1/t + 7

• t^4

• t + 4

How is the change in y calculated?

• By integrating t^4 from t=1 to t=3

• By adding t^4 to the initial position

• By multiplying t^4 by time

• By differentiating t^4 from t=1 to t=3

What is the position of the particle at t=3?

• (3.22, 52.4)

• (3, 4)

• (4, 3)

• (0, 0)

How is the magnitude of the total displacement calculated?

• By multiplying the changes in x and y

• Using the Pythagorean theorem

• By adding the changes in x and y

• By subtracting the changes in x and y

Why is the magnitude of the total displacement approximately equal to the change in y?

• Because the change in x is very small

• Because the velocity components are equal

• Because the initial position is at the origin

• Because the change in y is very small