Question

A racing cyclist is traveling at 19.3 km/h when she speeds up with a constant acceleration of 0.67m/s^2. What is her velocity after 5.00s?

Answer 1

We know that the accelaration is given by:

$a=\frac{v_f-v_0}{t}$

since we know the acceleration, the initial velocity and the time we can calculate the final velocity of the cyclist with this formula but before we do this we need to express the initial velocity in the m/s so that the units we use are consistent with each other. Let's make the conversion:

$19.3\frac{\operatorname{km}}{\text{ h}}\cdot\frac{1000\text{ m}}{1\text{ km}}\cdot\frac{1\text{ h}}{3600\text{ s}}=5.35\frac{\text{ m}}{\text{s}}$

Hence the initial velocity is 5.35 m/s.

Now that we have this we plug the values and solve for the final velocity:

$\begin{gathered} 0.67=\frac{v_f-5.35}{5} \\ v_f=(5)(0.67)+5.35 \\ v_f=8.71 \end{gathered}$

Therefore the velocity of the cyclist after five seconds is 8.71 m/s (this is the same as 31.36 km/h)