# Find the Initial Speed given Distance Traveled and Time Taken

I performed a lab where we needed to find the mathematical relationship between the starting speed (initial velocity) and the stopping distance.
However, I'm pretty sure we recorded all the initial speeds incorrectly. Is there a way to calculate the initial speed knowing the Distance Traveled and Time Taken? The data is as follows: (Friction is negligible for now)

1.9m----1.82s
3.2m----2.85s
3.4m----3.19s
3.1m----2.86s
3.9m----3.21s

Additional Information: The experiment was done with a car, the final velocity is 0.

Thanks a lot!

## Answers and Replies

Average velocity is equal to distance over time. Assuming your acceleration is constant, average velocity is equal to final plus initial over 2. Since your final velocity is 0, initial should be twice the average.

Δv = $\frac{v_{f}+v_{i}}{2}$ = $\frac{Δx}{t}$

Right, that makes sense, how would my equation change if I were to add friction?

It would be the same. Your negative acceleration is due to friction/drag. If there were no friction/drag acting against your car, there would be no acceleration and velocity would be constant (i.e. the car would keep going until it hit a wall).