Middle School

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Round the answer to the nearest tenth.

An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. What was the speed of the vehicle before the brakes were applied?

Answer :

The speed of the vehicle before the brake were applied was about 83.7 feet/s

Further explanation

Acceleration is rate of change of velocity.

[tex]\large {\boxed {v^2 = u^2 + 2ad}[/tex]

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

This problem is about accelerated motion.

Given:

final speed of the vehicle = v = 0 feet/s

length of skid marks = d = 175 feet

maximum deceleration = a = 20 feet/s² ( assumption )

Unknown:

initial speed = u = ?

Solution:

[tex]v^2 = u^2 - 2ad[/tex]

[tex]0^2 = u^2 - 2(20)(175)[/tex]

[tex]u^2 = 7000[/tex]

[tex]u = \sqrt{7000}[/tex]

[tex]u = 10\sqrt{70} \texttt{ feet/s}[/tex]

[tex]u \approx 83.7 \texttt{ feet/s} [/tex] (rounded to the nearest tenth)

[tex]\texttt{ }[/tex]

Conclusion:

The speed of the vehicle before the brake were applied was about 83.7 feet/s if we assume that maximum deceleration of the vehicle is about 20 feet/s²

[tex]\texttt{ }[/tex]

Learn more

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  • Acceleration : https://brainly.com/question/2283922
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Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

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Rewritten by : Jeany

Answer:

v2 - v02 = 2ad

v = final speed = 0 (came to a full stop)

v0 = initial speed (what you want to solve for)

d = stopping distance = 175 feet

Then

v0 = √(-2ad) [Remember a is negative, so the argument of the square root is positive.]

But as you can see, we need the acceleration.

If we knew the time it took to come to a full stop, we could still answer the question. Either way, we need more information than just the stopping distance.

Step-by-step explanation:


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