# Question #43247

Oct 13, 2017

$a = 6 \frac{m}{s} ^ 2$

#### Explanation:

The formula relating velocity under constant acceleration is:

${v}_{f} = {v}_{i} + a t$

Each variable, and the known values for this problem, are shown below:

$\left\{\begin{matrix}{v}_{f} & \text{Final velocity" & 22 m/s \\ v_i & "Initial velocity" & 4 m/s \\ a & "Acceleration" & "?" \\ t & "Time} & 3 s\end{matrix}\right.$

Substituting into the formula:

$22 \frac{m}{s} = 4 \frac{m}{s} + a \left(3 s\right)$

$18 \frac{m}{s} = a \left(3 s\right)$

$6 \frac{m}{s} ^ 2 = a$

Oct 13, 2017

$a = 6$m/${s}^{2}$

#### Explanation:

The velocity when roller coaster starts down the slope is $4$m/$s$.
That is, it's initial velocity is $4$m/$s$, i.e., $u = 4$

After $t = 3 s$ the velocity a the bottom is $22$m/$s$.
That is, it's final velocity is $22$m/$s$, i.e., $v = 4$

Using formula,
$v = u + a t$
$22 = 4 + 3 a$

$a = 6$m/${s}^{2}$