Uniform Acceleration

We are told the skateboarder starts from rest, so $u=0\text{ m/s}$. The acceleration is $a=3{\text{ m/s}}^2$ and the time is $t=5\text{ s}$. We need to find the final velocity $v$.

Since we know $u$, $a$, and $t$, and we want $v$, we use: $v=u+at$

$v=0+(3)(5)=15\text{ m/s}$

The skateboarder's final velocity is 15 m/s. This makes sense because gaining $3\text{ m/s}$ every second for 5 seconds gives $15\text{ m/s}$.

We need to find the final velocity of an object starting from rest with $a=3{\text{ m/s}}^2$ and $t=5\text{ s}$. The equation $v=u+at$ applies.

$v=0+3\times 5=15$, not $8$. The value 8 m/s might arise from incorrectly adding $3+5$, which is not how the equation works.

25 m/s might come from multiplying $5\times 5=25$, but $a=3{\text{ m/s}}^2$, not $5{\text{ m/s}}^2$. This is an incorrect substitution.

1.67 m/s could result from dividing $a$ by $t$, i.e. $3÷5$, but the formula requires multiplication, not division.

The only remaining option is 15 m/s, which is confirmed by $v=0+(3)(5)=15\text{ m/s}$.

Uniform acceleration means the acceleration is constant — it does not change over time. As a result, velocity increases (or decreases) by the same amount each second.

The word 'uniform' means 'the same'. So uniform acceleration = the same acceleration at every moment. This means equal changes in velocity per unit time.

The option 'Acceleration that remains constant over time, so velocity changes by the same amount every second' matches the definition precisely.

We need to find the correct definition of uniform acceleration from the four options given.

'An object moving at a constant velocity with no change in speed' describes zero acceleration, not uniform acceleration. This is incorrect.

'Acceleration that increases steadily over time' describes non-uniform or changing acceleration. Uniform means the acceleration value itself stays the same.

'Any motion where the object is speeding up' is too vague — an object can speed up with changing (non-uniform) acceleration. Uniform requires constant acceleration.

The correct definition is 'Acceleration that remains constant over time, so velocity changes by the same amount every second'.