Movement along a straight line w/vector functions

In summary, movement along a straight line with vector functions involves using vector functions to describe the position, velocity, and acceleration of an object as it moves along a straight line. This is represented by the position vector, velocity vector, and acceleration vector. The velocity vector describes both the speed and direction of the object's motion, while the acceleration vector describes the rate of change of the velocity vector. These three quantities are related through the fundamental theorem of calculus. This concept has many real-world applications, including describing the motion of objects in physics and engineering, analyzing traffic patterns, and predicting the paths of projectiles in sports or military situations.
  • #1
morsel
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Homework Statement


A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t = 0. The particle moves toward the point (3, 0, 3) with constant acceleration 2i + j + k. Find its position vector r(t) at time t.

Homework Equations


Speed = |v|

The Attempt at a Solution


v(t) = 2ti + tj + tk + c1
I don't know how to find c1 from here.

Thanks in advance!
 
Last edited:
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  • #2
c1 is v(0). c1 should be vector pointing along the direction from (1,-1,2) to (3,0,3) with length 2, right? Sure you can't find that?
 

FAQ: Movement along a straight line w/vector functions

1. What is movement along a straight line with vector functions?

Movement along a straight line with vector functions is a mathematical concept that involves describing the position, velocity, and acceleration of an object as it moves along a straight line using vector functions.

2. How is movement along a straight line represented with vector functions?

Movement along a straight line is represented using vector functions by the position vector, velocity vector, and acceleration vector. The position vector describes the location of the object at any given time, while the velocity vector describes the rate of change of the position vector and the acceleration vector describes the rate of change of the velocity vector.

3. What is the difference between speed and velocity in movement along a straight line with vector functions?

Speed is a scalar quantity that describes how fast an object is moving, while velocity is a vector quantity that describes both the speed and direction of an object's motion. In movement along a straight line with vector functions, the velocity vector is used to describe the object's speed and direction.

4. How are position, velocity, and acceleration related in movement along a straight line with vector functions?

In movement along a straight line with vector functions, position, velocity, and acceleration are related through the fundamental theorem of calculus. The position vector is the integral of the velocity vector, and the velocity vector is the integral of the acceleration vector.

5. What real-world applications does movement along a straight line with vector functions have?

Movement along a straight line with vector functions has many real-world applications, such as describing the motion of objects in physics and engineering, analyzing the movement of vehicles in traffic, and predicting the trajectories of projectiles in sports or military applications.

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