Calculus-Sec-12-4-Solution

12.4   Motion Along A Space Curve: Velocity and Acceleration

by SGLee - HSKim - JHLee

1-5. Find the velocity, acceleration, and speed of a particle with the given position function.

Sketch the path of the particle and draw the velocity and acceleration vectors for specified value of .

1.

6-10. Find the velocity, acceleration and speed of a particle with the given position function.

6.

,

,

.

7.

,

,

.

8.

,

,

.

9.

,

,

.

10.

,

,

.

11-12. Find the velocity and position vectors of a particle that has the given acceleration

and the given initial velocity and position.

11.

. Since , we have .

.

Since , we have .

12.

. Since , we have .

.

Since , we have .

13-14. Find the position vector of a particle that has the given acceleration

and the specified initial velocity and position.

13.

. Since ,

we have .

.

Since , we have .

14.

.

Since , we have .

.

Since , we have .

15. The position function of a particle is given by .

When is the speed a minimum?

16-20. Find the tangential and normal components of the acceleration vector.

16.