# Question #72067

Nov 6, 2017

The mass is $= 12.9 k g$

#### Explanation:

Apply the equation of motion

$v = u + a t$

to calculate the acceleration

The initial speed is $u = 0 m {s}^{-} 1$

The final speed is $v = 107 m {s}^{-} 1$

The time is $t = 2.3 s$

The acceleration is

$a = \frac{v - u}{t} = \frac{107 - 0}{2.3} = 46.52 m {s}^{-} 2$

According to Newton's second Law

$F = m a$

The force is $F = 600 N$

The mass is

$m = \frac{F}{a} = \frac{600}{46.52} = 12.9 k g$

Nov 6, 2017

12.897 kg, or 28.433 lb.

#### Explanation:

The formula for force, in Newtons $N$, is $F = m a$, where $F$ is the force, $m$ is the mass in $k g$, and $a$ is the acceleration in $m {s}^{-} 2$.

The formula for acceleration is $\frac{\Delta v}{\Delta t}$. Here, $\Delta v = 107 m {s}^{-} 1$ and $\Delta t = 2.3 s$.

So the acceleration is $46.522 m {s}^{-} 2$.

The formula for force can be rearranged thus:

$F = m a$

$\frac{F}{a} = \frac{m \cancel{\textcolor{red}{a}}}{\cancel{\textcolor{red}{a}}}$

$m = \frac{F}{a}$

$m = \frac{600}{46.522}$

$m = 12.897$

The required mass is 12.897 kg.