An object moves along the x-axis with a velocity given by va(t) A sin(wt), where W = = 3s-¹ and A = 1 m/s. (For an example of a physical scenario in which this type of behavior might occur, see question 4.) = (a) What is the displacement Ax of the object between t = 0 and t = ² s? Solve this graphically: Draw a graph of v vs. t for the indicated time range, and determine your answer entirely by examining this graph. - (b) What is the position r(t) of the object as a function of time if x(0) = 0 m? Solve this by direct integration: In other words, solve via x(t) − x(0) S v₂ (t')dt'. -
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.
Please include explanations and work
Given:-
The velocity of an object is given
where and A = 1 m/s
Find:-
a) What is the displacement of the object between the t = 0 and t = s? [Graphically solve]
b) What is the position x(t) of the object as a function of time if x(0) = 0 m
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