Question

A bike rider pedals with constant acceleration to reach a velocity of 7.8 m/s over a time of 5.7 s. during the period of acceleration, the bike's displacement is 18.75 m. what was the initial velocity of the bike?

Answer 1

-1.22 m/s

Step-by-step explanation:

To find the initial velocity, we will use the following equation:

`d=(1)/(2)(v_i+v_f)t`

Where d is the displacement, t is the time, vi is the initial velocity and vf is the final velocity.

So, replacing vf by 7.8 m/s, t by 5.7s, and d by 18.75 m, we get:

`18.75=(1)/(2)(v_i+7.8)(5.7)`

Now, we can solve for vi:

`\begin{gathered} (18.75)/(5.7)=(1)/(2)(v_i+7.8) \\ 3.29=(1)/(2)(v_i+7.8) \\ 3.29*2=v_i+7.8 \\ 6.58=v_i+7.8 \\ 6.58-7.8=v_i \\ -1.22m/s=v_i \end{gathered}`

Therefore, the initial velocity of the bike was -1.22 m/s