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in coming to a stop, a car leaves skid marks 65m long on a highway.assuming a deceleration of 4m/s^2,estimate the speed of the car just before breaking?

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btsangiie13280


Assuming a CONSTANT deceleration of 7.00 m/s^2,

final velocity, v = 0 m/s

acceleration, a = -7.00 m/s^2,

displacement, s = 92 m


using v^2 = u^2 + 2as

0^2 = u^2 + 2 (-7.00) (92)

initial velocity, u = sqrt (1288) = 35.9 m/s


This is the speed of the car just before braking.
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carlosego

By definition, we have that the final speed is given by:

\(vf ^ 2 = vo ^ 2 + 2ad
\)

Where,

vo: initial speed

a: acceleration

d: displacement

Substituting values we have:

\(0 ^ 2 = vo ^ 2 + 2 (-4) (65)
\)

From here, we clear the value of the initial velocity.

We have then:

\(0 = vo ^ 2 - 520

vo ^ 2 = 520
\)

\(vo = \sqrt{520}\)

\(vo = 22.8 \frac{m}{s}
\)

Answer:

The speed of the car just before breaking was:

\(vo = 22.8 \frac{m}{s}\)

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