If a stone is dropped from a height of 400 feet, its height s after t seconds is given by s(t) = 400 – 16t, with s in feet. (a) Compute s'(t). s'(t) = Find the stone's velocity at times t = 0, 1, 2, 3, and 4 seconds. s'(0) = | s'(1) = X ft/sec X ft/sec s'(2) = s'(3) = s'(4) = | X ft/sec X ft/sec X ft/sec (b) When does the stone reach the ground, and how fast is it traveling when it hits the ground? HINT [It reaches the ground when s(t) = 0.] The stone is traveling at a velocity of X ft/sec when it hits the ground at X seconds.
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.
![If a stone is dropped from a height of 400 feet, its heights after t seconds is given by s(t) = 400 – 16t, with s in feet.
(a) Compute s'(t).
s'(t) =
Find the stone's velocity at times t = 0, 1, 2, 3, and 4 seconds.
s'(0) =
s'(1) =|
s'(2) =
s'(3) =
X ft/sec
X ft/sec
× ft/sec
X ft/sec
X ft/sec
s'(4) =
(b) When does the stone reach the ground, and how fast is it traveling when it hits the ground? HINT [It reaches the ground when s(t) = 0.]
The stone is traveling at a velocity of
X ft/sec when it hits the ground at
X seconds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68cc5e62-1f1e-447e-86e2-72966307f0c4%2Fbfa842da-2012-4f71-9923-506e247a0484%2Ftts4tpb_processed.jpeg&w=3840&q=75)
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