Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 58

A motorist suddenly notices a stalled car and slams on the brakes, negatively accelerating at \(6.3 \mathrm{m} / \mathrm{s}^{2} .\) Unfortunately, this isn't enough, and a collision ensues. From the damage sustained, police estimate that the car was going \(18 \mathrm{km} / \mathrm{h}\) at the time of the collision. They also measure skid marks 34 m long. (a) How fast was the motorist going when the brakes were first applied? (b) How much time elapsed from the initial braking to the collision?

Short Answer

Expert verified
The initial velocity is calculated in Step 4 and the time elapsed from the initial breaking to the collision is calculated in Step 3. Both are dependent on solving the quadratic equation correctly in Step 3.

Step by step solution

01

Convert final velocity to m/s

The final velocity provided is in km/h. Let's convert it to m/s using the conversion factor 1 km/h = 0.2778 m/s. Therefore, \(18 km/h = 18 * 0.2778 = 5 m/s\)
02

Find initial velocity (u)

We know that \(v= u - at\), where a is actually -6.3 m/s^2 (negative as it is deceleration), and v is 5 m/s we calculated above. We can rearrange this equation to solve for u, getting: \(u = v + at\). But to use this equation, we need to know 't'. Let's find 't' first.
03

Find Time

Using the equation of motion \(s = ut + 0.5at^2\), we can rearrange the equation to solve for t by plugging in known values (s=34m, v=5m/s and a=-6.3m/s^2), yielding a quadratic equation: \(t^2 + (v/a)t - (s/a) = 0\). Solving this quadratic equation will give us value of t.
04

Insert t into the velocity equation

Now that we have t, we can insert the t value and known values of v and a, into the velocity equation \(u = v + at\) to find the initial velocity, u.
05

Conclusion

Now we have the initial velocity and the time elapsed from the initial breaking to the collision.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You allow 40 min to drive 25 mi to the airport, but you're caught in heavy traffic and average only \(20 \mathrm{mi} / \mathrm{h}\) for the first 15 min. What must your average speed be on the rest of the trip if you're to make your flight?

An object's position is given by \(x=b t+c t^{3},\) where \(b=1.50 \mathrm{m} / \mathrm{s}, \quad c=0.640 \mathrm{m} / \mathrm{s}^{3},\) and \(t\) is time in seconds. To study the limiting process leading to the instantaneous velocity, calculate the object's average velocity over time intervals from (a) \(1.00 \mathrm{s}\) to \(3.00 \mathrm{s},\) (b) \(1.50 \mathrm{s}\) to \(2.50 \mathrm{s},\) and \((\mathrm{c}) 1.95 \mathrm{s}\) to \(2.05 \mathrm{s}\) (d) Find the instantaneous velocity as a function of time by differentiating, and compare its value at 2 s with your average velocities.

An egg drops from a second-story window, taking 1.12 s to fall and reaching \(11.0 \mathrm{m} / \mathrm{s}\) just before hitting the ground. On contact, the egg stops completely in 0.131 s. Calculate the average magnitudes of its acceleration while falling and while stopping.

You're at mission control for a rocket launch, deciding whether to let the launch proceed. A band of clouds \(5.3 \mathrm{km}\) thick extends upward from \(1.9 \mathrm{km}\) altitude. The rocket will accelerate at \(4.6 \mathrm{m} / \mathrm{s}^{2},\) and it isn't allowed to be out of sight for more than \(30 \mathrm{s}\) Should you allow the launch?

Consider two possible definitions of average speed: (a) the average of the values of the instantaneous speed over a time interval and (b) the magnitude of the average velocity. Are these definitions equivalent? Give two examples to demonstrate your conclusion.
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Rotational Dynamics

Read Explanation

Kinematics Physics

Read Explanation

Fluids

Read Explanation

Modern Physics

Read Explanation

Astrophysics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free