A train traveling at vo = 20.0 m/s begins to brake by applying a velocity-dependent instantaneous acceleration m/s² a(v) = D = α where a = -22.0 m²/s³, v is the instantaneous velocity of the train, and u = 0.5 m/s. Determine the distance D traveled by the train before it comes to a complete stop. v +u Incorrect 125.758 m
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 train traveling at vo = 20.0 m/s begins to brake by applying a velocity-dependent insta < Feedback
m/s²
a(v) =
D =
where a = -22.0 m²/s3, v is the instantaneous velocity of the train, and u = 0.5 m/s.
Determine the distance D traveled by the train before it comes to a complete stop.
α
v+u
125.758
Incorrect
Use calculus to derive the equation
for the train's velocity as a function of
time from the explicit dependence of
the acceleration on velocity.
a (v) =
du
dt
=
α
(v +u)
α
(v +u)
(v +u) dv = (a) dt
Integrate both sides of this equation
to obtain an expression for u in terms
of t. Make sure to use appropriate
integration limits or boundary
conditions. Then, set v = 0 and solve
for the time it takes the train to stop.
Follow a similar procedure to obtain
an expression for distance as a
function of time. The resulting](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b319816-3828-4c3a-a4b8-8b6da6d278f2%2F08d8e7a7-61db-4ca6-bbff-804ef38bc56d%2F1192n5d_processed.jpeg&w=3840&q=75)
![A train traveling at vo = 20.0 m/s begins to brake by applying a velocity-dependent instantaneous acceleration
m/s²
a(v) =
D =
a
where a = -22.0 m²/s3, v is the instantaneous velocity of the train, and u = 0.5 m/s.
Determine the distance D traveled by the train before it comes to a complete stop.
v +u
Incorrect
125.758
m](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b319816-3828-4c3a-a4b8-8b6da6d278f2%2F08d8e7a7-61db-4ca6-bbff-804ef38bc56d%2Fl5d5v6u_processed.jpeg&w=3840&q=75)
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