Particle Motion in the XY Plane

The video tutorial explains the motion of a particle in the XY plane using parametric functions for position and velocity. It focuses on finding the x-coordinate of the particle at time T=2 by integrating the velocity function. The tutorial demonstrates using a calculator to evaluate the definite integral, emphasizing the importance of being in radian mode.

What is the initial position of the particle at time T=1?

• (1, 1)

• (3, 5)

• (0, 0)

• (5, 3)

Which function represents the x-component of the velocity vector?

• cosine of T^2

• sine of T

• e to the 0.5T

• T^2

How do you calculate the change in x-coordinate from T=1 to T=2?

• By adding the initial x-coordinate to the y-component of the velocity

• By subtracting the y-component of the velocity at T=1 from T=2

• By integrating the x-component of the velocity from T=1 to T=2

• By multiplying the velocity by the time interval

What mathematical operation is used to find the displacement in the x-direction?

• Multiplication

• Differentiation

• Addition

• Integration

What is the final x-coordinate of the particle at T=2?

• Exactly 5

• Approximately 2.55

• Exactly 3

• Approximately 5.55