Question

A particle starts from rest and accelerates uniformly in a straight line. The particle travels a distance of 6.70 m in 2.50 s .

How fast, in miles/hour (mph), will the particle be traveling after a time of 4.50 s has elapsed? Assume 1 mile=1609.34 m.

Express your answer using three significant figures.

Answer 1

Since particle starts from rest ,initial velocity is zero

Distance traveled in 2.5 s = 6.7m

Use formula $s=ut+1/2at^{2}$ to find acceleration

$6.7m=(0m/s)(2.5s)+1/2a(2.5s)^{2}$

$6.7=0*2.5+0.5*a*2.5^{2}$

$6.7=3.125a$

${\color{Red} a=2.144m/s^{2}}$

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Use formula $v=u+at$ to find speed after 4.5s

$v=0m/s+(2.144m/s^{2})(4.5s)$

$v=0+2.144*4.5$

${\color{Red} v=9.648m/s}$

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Given 1 mile=1609.34 m

1 hr =3600s

$9.648m/s=9.648m/s*1*1$

$9.648m/s=9.648\frac{{\color{Red} m}}{{\color{Blue} s}}*\frac{1mile}{1609.34{\color{Red} m}}*\frac{3600{\color{Blue} s}}{1hr}$

$9.648m/s=9.648*3600*\frac{1}{1609.34}*\frac{mile}{hr}$

$9.648m/s=21.582mi/hr$

ANSWER: ${\color{Red} 21.6mi/hr}$

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