- #1
jmagic
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Homework Statement
Homework Equations
i+j+k=1, <1,1,1>
The Attempt at a Solution
a(t)=i+(30t^(4))j+(2e^(-t)ln(e)-2e^(-t)(1/e))k
r(t)=(2+6t)i+(2+t^6+2t)j+(2+2e^-t)k
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1. The problem statement, a
jmagic said:r(t)=(2+6t)i+(2+t^6+2t)j+(2+2e^-t)k
a(t)=i+(30t^(4))j+(2e^(-t)ln(e)-2e^(-t)(1/e))k
Vector velocity in 3D refers to the speed and direction of an object in three-dimensional space. It is a vector quantity that takes into account both the magnitude (speed) and direction of an object's motion.
To calculate vector velocity in 3D, you need to know the object's position at two different points in time. Then, you can use the displacement (change in position) and the time interval to calculate the average velocity vector. This can be represented using vector notation, with the magnitude being the distance traveled and the direction being the change in position.
Speed is a scalar quantity that only considers the magnitude of an object's motion, while velocity is a vector quantity that takes into account both the magnitude and direction of an object's motion. This means that an object can have the same speed but different velocities if they are moving in different directions.
In 3D space, vector velocity can be represented using vector arrows. The length of the arrow represents the magnitude (speed) of the object's motion, while the direction of the arrow represents the direction. The arrows can also be drawn on a coordinate system to show the position and orientation of the object in space.
Some real-life examples of vector velocity in 3D include the motion of airplanes, satellites, and projectiles. These objects all have both speed and direction in three-dimensional space, making them perfect examples of vector velocity. Another example could be the motion of a person swimming in a pool, where their speed and direction change as they move through the water in three dimensions.