# How to Calculate the Initial Velocity of a Bike with Constant Acceleration

## What are the steps to calculate the initial velocity of a bike with constant acceleration?

Let's break down the process of determining the initial velocity based on the final velocity, acceleration, time, and displacement.

### Final answer:

To find the initial velocity of the bike with constant acceleration, we use kinematic equations that incorporate the given final velocity, acceleration, time, and displacement. We calculate the acceleration first and then solve for the initial velocity.

### Explanation:

**Finding the Initial Velocity of the Bike**

To determine the initial velocity of the bike, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, displacement, and time:

vf = vi + at

d = vi*t + (1/2)at²

Given that the final velocity (vf) is 7.5 m/s, acceleration time (t) is 4.5 s, and displacement (d) is 19 m, we can solve for the initial velocity (vi). Using the second equation, we rearrange to solve for vi:

vi = (d - (1/2)at²) / t

We know the displacement and time, but we need to find acceleration (a) first. We use the first equation to find acceleration:

7.5 m/s = vi + a(4.5 s)

Since we don't have vi yet, we use this equation after finding acceleration with the displacement:

19 m = vi(4.5 s) + (1/2)a(4.5 s)²

From the above information, we can calculate acceleration and then use that to find the initial velocity. By following these calculations, you will understand the steps to find the initial velocity of a bike when given its final velocity, acceleration, time, and displacement.