Find the Initial Speed given Distance Traveled and Time Taken

[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!

 

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

 

[Shauta]

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

 

[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).

 

[Nickie]

Yes, there is a way to calculate the initial speed given the distance traveled and time taken. This can be done using the formula v = d/t, where v is the initial speed, d is the distance traveled, and t is the time taken. In this case, since the final velocity is 0, we can assume that the car has come to a complete stop and the initial velocity is equal to the final velocity. Therefore, we can use the formula v = d/t to calculate the initial speed for each trial in the experiment.

For example, for the first trial where the distance traveled is 1.9m and the time taken is 1.82s, the initial speed would be calculated as v = 1.9m/1.82s = 1.04 m/s. Similarly, for the other trials, the initial speeds would be calculated as follows:

- Trial 1: v = 1.9m/1.82s = 1.04 m/s
- Trial 2: v = 3.2m/2.85s = 1.12 m/s
- Trial 3: v = 3.4m/3.19s = 1.07 m/s
- Trial 4: v = 3.1m/2.86s = 1.08 m/s
- Trial 5: v = 3.9m/3.21s = 1.22 m/s

It is important to note that these calculations assume that the car was traveling at a constant speed throughout the experiment. If there were any variations in speed during the trials, the initial speeds calculated using this method may not be accurate. It would be helpful to review the data and ensure that the car was traveling at a constant speed in each trial before using this formula to calculate the initial speed.