Question

A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a = a₁ + Fm where a₁ = 3.00 meter/second², F = 12.0 kilogram⋅meter/second² and m =7.00 kilogram. First, which of the following is the correct step for obtaining a common denominator for the two fractions in the expression in solving for a?
a. (m/m times a₁/1) + (1/1 times F/m)
b. (1/m times a₁/1) + (1/m times F/m)
c. (m/m times a₁/1) + (F/F times F/m)
d. (m/m times a₁/1) +(m/m times F/m )

Answer 1

Answer:

The correct option is option (a).

The acceleration of an object is $\frac{33}{7}$ m/s².

Explanation:

Given expression is

$a=a_1+\frac Fm$

[ divide a whole number by 1 to turn into a fraction. Since $a_1$ is a whole number, so  $a_1$  is divided by 1 to turn into a fraction]

$\Rightarrow a=\frac{a_1}{1}+\frac Fm$

[The l.c.m of the denominators 1 and m is m. Now multiply both numerator and denominator by m of $\frac{a_1}1$ and multiply both numerator and denominator by 1 of $\frac Fm$]

$\Rightarrow a=(\frac mm\times\frac{a_1}{1})+(\frac 11\times\frac Fm)$

The correct option is option (a)

Given that,

F= 12.0 kg.m/s² , m=7.00 kg and $a_1$ = 3.00 m/s²

$\therefore a=(\frac mm\times\frac{a_1}{1})+(\frac 11\times\frac Fm)$

     $=(\frac{7.00}{7.00}\times \frac{3.00}{1})+(\frac11\times \frac{12.0}{7.00})$

    $=\frac{21}{7}+\frac{12}{7}$

    $=\frac{21+12}{7}$

    $=\frac{33}{7}$ m/s²

The acceleration of an object is $\frac{33}{7}$ m/s².