# Two objects move with initial velocity -9.15 m/s, final velocity 18.3 m/s, and constant accelerations.The first object has displacement 19.5 m. What is its acceleration? The second object travels a total distance of 22.5 m. What is its acceleration?

Jun 12, 2015

${a}_{1} = 6.44 \frac{m}{s} ^ 2$,

${a}_{2} = 5.58 \frac{m}{s} ^ 2$.

#### Explanation:

The two laws of the accelerated motion are:

$s = {s}_{0} + {v}_{0} t + \frac{1}{2} a {t}^{2}$

and

$v = {v}_{0} + a t$.

But if you solve the system of the two equations, you can find a third law really useful in those cases in which you haven't the time, or you haven't to find it.

${v}^{2} = {v}_{0}^{2} + 2 a \Delta s$ in which $\Delta s$ is the space run.

So:

$a = \frac{{v}^{2} - {v}_{0}^{2}}{2 \cdot \Delta s} = \frac{{18.3}^{2} - {\left(- 9.15\right)}^{2}}{2 \cdot 19.5} = 6.44 \frac{m}{s} ^ 2$,

$a = \frac{{v}^{2} - {v}_{0}^{2}}{2 \cdot \Delta s} = \frac{{18.3}^{2} - {\left(- 9.15\right)}^{2}}{2 \cdot 22.5} = 5.58 \frac{m}{s} ^ 2$.