4. The position of an object in three dimensions as a function of time is given by 7 = (at? + bt)î + ct?} + dk Where i, j and k are the unit vectors in the x, y and z directions respectively. The parameters take the following values: a = 2.36 m/s? b = - 1.21 m/s c = 5.82 m/s? d = - 4.48 m a) What is the speed of the object at times t= 2.66s? b) Find the time when the instantaneous acceleration a and the instantaneous velocity v vectors are orthogonal.
Displacement, Velocity and Acceleration
In classical mechanics, kinematics deals with the motion of a particle. It deals only with the position, velocity, acceleration, and displacement of a particle. It has no concern about the source of motion.
Linear Displacement
The term "displacement" refers to when something shifts away from its original "location," and "linear" refers to a straight line. As a result, “Linear Displacement” can be described as the movement of an object in a straight line along a single axis, for example, from side to side or up and down. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Non-contact sensors such as LVDTs and other linear location sensors can calculate linear displacement. Linear displacement is usually measured in millimeters or inches and may be positive or negative.
![4. The position of an object in three dimensions as a function of time is given by
Ť = (at? + bt)î + ct²} + dk
Where i, j and k are the unit vectors in the x, y and z directions respectively.
The parameters take the following values:
a = 2.36 m/s?
b = - 1.21 m/s
c = 5.82 m/s?
d = - 4.48 m
a) What is the speed of the object at times t= 2.66s?
b) Find the time when the instantaneous acceleration a and the instantaneous velocity v
vectors are orthogonal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ec70b84-8e2a-4846-85d9-f50115a864e8%2F720057bb-4a15-4edd-a2c3-7c5bf27c98be%2Fn7c84c5_processed.jpeg&w=3840&q=75)
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