Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q. 52 (page 62)

The minimum stopping distance for a car traveling at a speed

of 30 m/s is 60 m, including the distance traveled during the

driver’s reaction time of 0.50 s. What is the minimum stopping distance for the same car traveling at a speed of 40 m/s?

Short Answer

Expert verified

Minimum stopping distance travelled by the car at a speed of40m/sis100m.

Step by step solution

01

Given information

Speed of the car is u=30m/s.

Stopping distance of the car with this speed isD=60m.

Reaction time taken by the driver, t=0.50s.

02

Calculation of the distance travelled while deacceleration

During reaction time, the distance travelled by the driver is,

x=utx=30×0.50mx=15m

Therefore, while slowing down, distance travelled by the driver is,

s=D-xs=60-15ms=45m

03

Calculation of stopping distance

Initial acceleration of the car can be calculated as,

0=u2+2asa=-u22sa=-3022×45a=-10m/s2

Now, considering the initial speed as u'=40m/s,distance travelled by the car during constant motion is,

s1=u'ts1=40×0.5ms1=20m

The distance travelled by the car during slowing down can be obtained as,

0=u'2+2as2s2=-u'22as2=-4022-10ms2=80m

Therefore, minimum stopping distance should be,

S=s1+s2S=20+80mS=100m

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

Careful measurements have been made of Olympic sprinters

in the 100 meter dash. A quite realistic model is that the sprinter’s

velocity is given by

vx=a(1-e-bt)

where t is in s, vx is in m/s, and the constants a and b are characteristic

of the sprinter. Sprinter Carl Lewis’s run at the 1987

World Championships is modeled with a = 11.81 m/s and

b = 0.6887 s-1.

a. What was Lewis’s acceleration at t = 0 s, 2.00 s, and 4.00 s?

b. Find an expression for the distance traveled at time t.

c. Your expression from part b is a transcendental equation,

meaning that you can’t solve it for t. However, it’s not hard to

use trial and error to find the time needed to travel a specific

distance. To the nearest 0.01 s, find the time Lewis needed to

sprint 100.0 m. His official time was 0.01 s more than your

answer, showing that this model is very good, but not perfect.

A particle’s velocity is described by the function vx = kt 2 m/s, where k is a constant and t is in s. The particle’s position at t0 = 0 s is x0 = - 9.0 m. At t1 = 3.0 s, the particle is at x1 = 9.0 m. Determine the value of the constant k. Be sure to include the proper units

FIGURE Q2.4 shows a position-versus-time graph for the motion of

objects A and B as they move along the same axis.

a. At the instant t = 1 s, is the speed of A greater than, less than,

or equal to the speed of B? Explain.

b. Do objects A and B ever have the same speed? If so, at what

time or times? Explain.

The position of a particle is given by the function x=2t3-6t2+12m, where t is in s. a. At what time does the particle reach its minimum velocity? What is Vxmin? b. At what time is the acceleration zero?

When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation
vx2=2Pmt
where P = 3.6 * 104 watts is the car’s power output, m = 1200 kg is its mass andvx is in m/s. That is, the square of the car’s velocity increases linearly with time.
a. Find an algebraic expression in terms of P, m, and t for the car’s acceleration at time t.
b. What is the car’s speed at t = 2 s and t = 10 s?
c. Evaluate the acceleration at t = 2 s and t = 10 s
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Wave Optics

Read Explanation

Force

Read Explanation

Energy Physics

Read Explanation

Particle Model of Matter

Read Explanation

Geometrical and Physical Optics

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