Question

a bicyclist, initially at rest, begins pedaling and gaining speed steadily for 6.20s during which she covers 39.0m. what was her final speed? m/s

Explanation:

Step1: Recall the kinematic - equation for average speed

The average speed formula for uniformly - accelerated motion is $v_{avg}=\frac{v_0 + v}{2}$, and the displacement formula is $x = v_{avg}t$. Since the bicyclist starts from rest, $v_0 = 0$.

Step2: Substitute the average - speed formula into the displacement formula

We know that $x=\frac{v_0 + v}{2}t$. Substituting $v_0 = 0$ into the formula, we get $x=\frac{0 + v}{2}t=\frac{v}{2}t$.

Step3: Solve for the final speed $v$

We can re - arrange the equation $x=\frac{v}{2}t$ to solve for $v$. Multiply both sides of the equation by $\frac{2}{t}$, so $v=\frac{2x}{t}$.
Given $x = 39.0m$ and $t = 6.20s$, then $v=\frac{2\times39.0}{6.20}\ m/s$.
$v=\frac{78.0}{6.20}\ m/s\approx12.6\ m/s$

Answer:

$12.6$