A particle starts from the origin with velocity 5 i ^ m / s at t = 0 and moves in the xy plane with a varying acceleration given by a → = ( 6 t j ^ ) , where a → is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function of time. (b) Determine the position of the particle as a function of time.
A particle starts from the origin with velocity 5 i ^ m / s at t = 0 and moves in the xy plane with a varying acceleration given by a → = ( 6 t j ^ ) , where a → is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function of time. (b) Determine the position of the particle as a function of time.
Solution Summary: The author explains the velocity of the particle as a function of time.
A particle starts from the origin with velocity
5
i
^
m
/
s
at t = 0 and moves in the xy plane with a varying acceleration given by
a
→
=
(
6
t
j
^
)
, where
a
→
is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function of time. (b) Determine the position of the particle as a function of time.
The equation r(t) = ( sin t)i + ( cos t)j + (t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors.
π
Then write the particle's velocity at t=
as a product of its speed and direction.
The velocity vector is v(t) = (i+j+ k.
A particle is moving in three dimensions and its position vector is given by;
r(t) = (4t² + 1.7t) î + (1.5t − 2.1)ĵ + (2.7t³ + 2t) k
where r is in meters and t is in seconds. Determine the magnitude of the instantaneous velocity at t = 3s. Express your answer in units of m/s using one decimal
place.
Answer:
Problem 2: The position of a particle is given by the following expression, where t is time
measured in seconds: r(t) = [(3.65 m/s?)f²]į+ (-4.23 m)j + [(4.48 m/s³)r*]k.
Part (a) What is the magnitude of the velocity of the particle, in m/s, at t = 0.00 s?
Part (b) What is the magnitude of the velocity of the particle, in m/s, at t = 1.65 s?
Part (c) What angle, in degrees, does the velocity of the particle make with the +z axis at t =
1.65 s?
Part (d) What is the magnitude of the average velocity, in m/s, betweent = 0.00 s and t = 1.65
s?
Part (e) What angle, in degrees, does the average velocity between t = 0.00 s and t = 1.65 s
make with the z axis?
Chapter 4 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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