Use the given information to find the position and velocity vectors of the particle.
a
(
t
)
=
i
+
e
−
t
j;
v(0)
=
2
i+j;
r(0)
=
i
−
j
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find the velocity, acceleration, and speed of a particle with the given position;
r(t) = ti + t²j + 2k. Sketch the path of the particle and draw the velocity and acceleration vectors
for t=1.
The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity and acceleration vectors. Then find the particle's speed and direction of motion at t= 1. Write the particle's velocity at that time as the product of its
speed and direction.
+²
r(t) = (3 In (t + 1))i + t²j+ -k
The velocity vector is v(t) =i+ i+
(Type exact answers, using radicals as needed.)
The acceleration vector is a(t) = i +
+ lk.
(Type exact answers, using radicals as needed.)
The velocity vector at t = 1 written as a product of the speed and direction is v(1) = () [(i+j+ k].
(Type an exact answer, using radicals as needed.)
The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity and acceleration vectors. Then find the particle's speed and direction of motion at t= 2. Write the particle's velocity at that time as the product of its speed and direction.
r(t) = (3 In (t + 1))i +*j+k
The velocity vector is v(t) = i+ j+ k
(Type exact answers, using radicals as needed.)
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