Let s(t) = t3 - 30t2 + 18t + 47 be the position function of a car moving along a horizontal line, where t is in seconds and s is in meters. a) Determine the interval when the car is moving to the left. b) Determine the car’s position relative to the origin at the instant if the acceleration is 4 m/s^2 . c) When is the car’s acceleration positive?
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.
Let s(t) = t3 - 30t2 + 18t + 47 be the position function of a car moving along a horizontal line, where t is in seconds and s is in meters.
a) Determine the interval when the car is moving to the left.
b) Determine the car’s position relative to the origin at the instant if the acceleration is 4 m/s^2 .
c) When is the car’s acceleration positive?
d) Determine if the speed of the car is increasing or decreasing at t = 4.5 seconds?
e) When is the car’s acceleration negative?
f) Calculate for the total distance traveled by the car during the first 5 seconds.
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