If r(t) = x(t)i + y(t)j + z(t)k, then r''(t) = x''(t)i + y''(t)j + z''(t)k.mamma_mia66 said:Homework Statement
Given [tex]\vec{}[/tex]r"(t)= 6i-4cos (2t)j+ 9e3tk,
r'[tex]\vec{}[/tex] (0)= 4i +3k and r[tex]\vec{}[/tex](0)=j+k, find r[tex]\vec{}[/tex](t).
Homework Equations
The Attempt at a Solution
I will appreciate any ideas how to start this problem. Thank you.
"r(t)" represents the position of an object at a given time "t". It is a vector quantity that includes both magnitude and direction.
Initial conditions refer to the starting values of a system or process. In the context of finding "r(t)", initial conditions would include the initial position and velocity of the object.
To find "r(t)", you would first need to know the initial conditions of the object, such as its initial position and velocity. Then, you would use equations of motion, such as the kinematic equations, to calculate the position of the object at a given time "t".
Yes, "r(t)" can be negative. This would indicate a position in the opposite direction of a reference point. However, it is important to keep in mind the direction of the coordinate system being used.
Finding "r(t)" can be useful in a variety of fields, such as physics, engineering, and astronomy. It can be used to track the position of objects in motion, predict their future positions, and analyze their motion over time. For example, it can be used to track the trajectory of a rocket, the movement of a satellite, or the path of a moving car.