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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 2 / Problem 18E

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Answer: CALC The position of the front bumper of a test

Chapter 2, Problem 18E

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QUESTION:

Problem 18E

CALC The position of the front bumper of a test car under microprocessor control is given by x(t) = 2.17 m + (4.80 m/s2)t2 - 1 0.100 m/s6)t6. (a) Find its position and acceleration at the instants when the car has zero velocity. (b) Draw x-t , vx-t , and ax-t graphs for the motion of the bumper between t = 0 and t = 2.00 s.

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QUESTION:

Problem 18E

CALC The position of the front bumper of a test car under microprocessor control is given by x(t) = 2.17 m + (4.80 m/s2)t2 - 1 0.100 m/s6)t6. (a) Find its position and acceleration at the instants when the car has zero velocity. (b) Draw x-t , vx-t , and ax-t graphs for the motion of the bumper between t = 0 and t = 2.00 s.

ANSWER:

Solution 18E

(a).To find x position of something at time T,the formula is:

$x(t)={x}_{0}+{v}_{0}*t+(1/2)a{t}^{2}$

Where ${x}_{0}$ =initial position

${v}_{0}=$ initial velocity in x-direction

a=acceleration

t=time

$x(t)=2.17+(4.80\ m/{s}^{2}){t}^{2}-(0.100){t}^{6}(m)$

$v(t)=x'(t)=2*(4.80)*t-6*(0.100){t}^{5}=(9.6\ )t-(0.600){t}^{5}(m/s)$

$a(t)=v'(t)=x"(t)=9.6-5*0.6{t}^{4}=9.6-3{t}^{4}$

Position at the instants when the car has zero velocity.

$v(t)=t*(9.6-0.6{t}^{4})=0$

$\Rightarrow{}t=0\ and\ 0.6{t}^{4}=9.6$

$\Rightarrow{}t=0\ and\ {t}^{2}=4.2$

$\Rightarrow{}t=0\ and\ t=1.54$

$\Rightarrow{}first\ instant\ (t=0)$

$x(0)=2.17\ m$

$\Rightarrow{}second\ instant\ (t=1.54)$

$x(1.54)=15\ m$

Acceleration at the instants when the car has zero velocity.

$\Rightarrow{}first\ instant(t=0)$

$a(0)=9.6\ m/{s}^{2}$

$\Rightarrow%$

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