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

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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
Transcribed Image Text: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
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
Transcribed Image Text: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
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