Question

A cyclist has a uniform acceleration of 2.30m/s^2. What distance will he need to travel in order to obtain a velocity of 21.0m/s if he started at rest?

Answer 1

To find the distance traveled by the cyclist, we can use the kinematic equation:

$v^2=u^2+2as$

Where:

• $v$ is the final velocity (21.0 m/s in this case)
• $u$ is the initial velocity (0 m/s, as the cyclist starts from rest)
• $a$ is the acceleration (2.30 m/s^2 in this case)
• $s$ is the distance traveled

Rearranging the equation, we have:

$s=\frac{v^2-u^2}{2a}$

Substituting the given values, we get:

$s=\frac{(21.0\text{m/s}{)}^2-(0\text{m/s}{)}^2}{2\times 2.30{\text{m/s}}^2}$

Simplifying the equation further:

s=441.0 m2/s24.60 m/s2s = frac{441.0, ext{m}^2/ ext{s}^2}{4.60, ext{m/s}^2}s=<span class="sizing reset-size6 size3 m