A particle is moving along a line with position given by s(t)=t3−(9/2(t2 ))+6t−5 measured in meters, with t≥0 measured in minutes, and the positive direction meaning forward. a) Find the equation for the velocity at time t. Give units, and find times the times the particle is moving forward. b) Find the equation for the velocity at time t. Give units, and find times the times the particle is moving backwards. c) Find the total distance travelled by the particle. d) Find the equation of the acceleration at time t. Give the units, and find the times when the velocity of the particle is not changing. e) Find the displacement.
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.
A particle is moving along a line with position given by s(t)=t3−(9/2(t2 ))+6t−5 measured in meters, with t≥0 measured in minutes, and the positive direction meaning forward.
a) Find the equation for the velocity at time t. Give units, and find times the times the particle is moving forward.
b) Find the equation for the velocity at time t. Give units, and find times the times the particle is moving backwards.
c) Find the total distance travelled by the particle.
d) Find the equation of the acceleration at time t. Give the units, and find the times when the velocity of the particle is not changing.
e) Find the displacement.
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