Problem 1. You are driving at 31.0 m/s when the truck ahead of you comes to a halt 200.0 m away fromyour bumper. Your brakes are in poor condition and you decelerate at a constant rate of 2.5 m/s.(a) How close do you come to the bumper of the truck?(b) How long does it take you to come to a stop?(c) Graph v versus t for the motion.

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Description: Problem 1. You are driving at 31.0 m/s when the truck ahead of you comes to a halt 200.0 m away fromyour bumper. Your brakes are in poor condition and you decelerate at a constant rate of 2.5 m/s.(a) How close do you come to the bumper of the truck?

Answered: Problem 1. You are driving at 31.0 m/s…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Problem 1. You are driving at 31.0 m/s when the truck ahead of you comes to a halt 200.0 m away from
your bumper. Your brakes are in poor condition and you decelerate at a constant rate of 2.5 m/s.
(a) How close do you come to the bumper of the truck?
(b) How long does it take you to come to a stop?
(c) Graph v versus t for the motion.

Expert Solution

Step 1 Distance from the bumper of truck

Equations of kinematics are as follow:

$v^{2} = u^{2} + 2 a d 1) v = u + a t 2) w h e r e, v = f i n a l v e l o c i t y u = i n i t i a l v e l o c i t y a = a c c e l e r a t i o n t = t i m e d = d i s \tan c e$

Values given in the question are as follow:

$d = 200 m v = 31 \frac{m}{s} a = - 2.5 \frac{m}{s^{2}}$

Distance traveled by your vehicle before comes at rest,

Substitute known values in equation-1):

$0 = {(31 \frac{m}{s})}^{2} + (2 \times (- 2.5 \frac{m}{s^{2}}) \times d_{1}) d_{1} = \frac{961}{5} m d_{1} = 192.2 m$

Distance between you and truck when your vehicle comes to rest,

$s = 200 - 192.2 s = 7.8 m$

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