# Vehicle Dynamics (AME 451) Chapter 12th Solutions

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Chapter 12 Solutions

University

University of Arizona

Course

Vehicle Dynamics (AME 451)

If a particle has an initial velocity of v0 = 12 ft>s to the

right, at s

0 = 0, determine its position when t = 10 s, if

a = 2 ft>s2 to the left.

12–3.

A particle travels along a straight line with a velocity

v = (12 – 3t2) m>s, where t is in seconds. When t = 1 s, the

particle is located 10 m to the left of the origin. Determine

the acceleration when t = 4 s, the displacement from

t = 0 to t = 10 s, and the distance the particle travels during

this time period.

A particle travels along a straight line with a constant

acceleration.When , and when ,

v = 8 ft>s.Determine the velocity as a function of position.

s = 4 ft v = 3 ft>s s = 10 ft

The velocity of a particle traveling in a straight line is given

by v = (6t – 3t2) m>s, where t is in seconds. If s = 0 when

t = 0, determine the particle’s deceleration and position

when t = 3 s. How far has the particle traveled during the

3-s time interval, and what is its average speed?

The position of a particle along a straight line is given by

, where t is in seconds.

Determine the position of the particle when and the

total distance it travels during the 6-s time interval. Hint:

Plot the path to determine the total distance traveled.

A particle moves along a straight line such that its position

is defined by s = (t2 – 6t + 5) m. Determine the average

velocity, the average speed, and the acceleration of the

particle when t = 6 s.

A particle is moving along a straight line such that its

position is defined by , where t is in

seconds. Determine (a) the displacement of the particle

during the time interval from to , (b) the

average velocity of the particle during this time interval,

and (c) the acceleration when t = 1 s.

t = 1 s t = 5 s

s = (10t2 + 20)

The acceleration of a particle as it moves along a straight

line is given by a = (2t – 1) m>s2, where t is in seconds. If

s = 1 m and v = 2 m>s when t = 0, determine the

particle’s velocity and position when t = 6 s. Also,

determine the total distance the particle travels during this

time period.

A particle moves along a straight line with an acceleration

of , where s is in meters.

Determine the particle’s velocity when , if it starts

from rest when .Use a numerical method to evaluate

the integral.

s = 1m

s = 2 m

a = 5>(3s1>3 + s5>2) m>s2

A particle travels along a straight-line path such that in 4 s

it moves from an initial position sA = -8 m to a position

sB = +3 m. Then in another 5 s it moves from sB to

sC = -6 m. Determine the particle’s average velocity and

average speed during the 9-s time interval.

Traveling with an initial speed of a car accelerates

at along a straight road. How long will it take to

reach a speed of Also, through what distance

does the car travel during this time?

120 km>h?

6000 km>h2

70 km>h

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