# Find the Initial Speed given Distance Traveled and Time Taken

1. Mar 17, 2013

### Shauta

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!

2. Mar 17, 2013

### djh101

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

3. Mar 17, 2013

### Shauta

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

4. Mar 17, 2013

### djh101

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).