How to expand the expressions 6(3+4w)
2 answers:
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Answer:
a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).
Step-by-step explanation:
a) Let is find first the velocity vector by differentiation:
Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:
Then,
Hence, the particle has a constant speed of 4.
b) The acceleration vector is obtained by deriving the velocity vector.
Velocity and acceleration are orthogonal to each other only if . Then,
Which demonstrates the orthogonality between velocity and acceleration vectors.
c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is:
And cosine decrease and sine increase inasmuch as t becomes bigger.
d) Let evaluate the vector in .
False, the particle begin at the point (0,1).