SUVAT Equations and Applications

Write out all five variables: s = ?, u = 0 m/s (starts from rest), v = ?, a = 2 m/s², t = 5 s. We need to find v, and the missing variable we don't need is s.

Since s is not needed, use the equation that excludes s: $v=u+at$

$v=0+(2)(5)=10\text{ m/s}$

The final velocity is 10 m/s. The unit m/s is correct for velocity.

We need the final velocity of an object starting from rest with $a=2{\text{ m/s}}^2$ for $t=5\text{ s}$. Using $v=u+at=0+2\times 5=10\text{ m/s}$.

25 m/s would result from using $s=\frac{1}{2}a{t}^2=\frac{1}{2}(2)(25)=25$, but this gives displacement, not velocity.

7 m/s has no basis in the correct application of any SUVAT equation with these values — it is simply incorrect.

2.5 m/s comes from dividing $a$ by $t$ rather than multiplying: $\frac{2}{5}=0.4$, not even 2.5. This is a misapplication of the equation.

10 m/s is the only value consistent with $v=u+at=0+(2)(5)=10\text{ m/s}$.

Each SUVAT equation is missing one variable. The four missing variables are: s (in $v=u+at$), v (in $s=ut+\frac{1}{2}a{t}^2$), t (in $v^2=u^2+2as$), and a (in $s=\frac{(u+v)}{2}t$).

The equation missing t is $v^2=u^2+2as$. It contains only s, u, v, and a — no t appears anywhere in the equation.

$v^2=u^2+2as$ is the correct choice. This equation is particularly useful when time is not known and not required.

We need to find the SUVAT equation that contains no t variable at all.

$v=u+at$ contains t explicitly — it cannot be the answer.

$s=ut+\frac{1}{2}a{t}^2$ contains t in two terms — it clearly involves time.

$s=\frac{(u+v)}{2}t$ also contains t — it requires time to calculate displacement.

$v^2=u^2+2as$ is the only equation with no t. It links v, u, a, and s only.