Result:
The information at hand includes:
The acceleration stands at 3.2 m/s² for a duration of 14 seconds.
Initial velocity is 5.1 m/s.
Starting position is 0m.
Therefore:
A(t) = 3.2m/s²
To derive the velocity, integration over time is performed where the constant of integration equals the initial velocity.
V(t) = (3.2m/s²)*t + 5.1 m/s
For the position equation, we integrate again over time, with the integration constant being the initial position (which is zero).
P(t) = (1/2)*(3.2 m/s²)*t² + 5.1m/s*t
The final position corresponds to when the car ceases to accelerate, occurring at t = 14s.
P(14s) = (1/2)*(3.2 m/s²)*(14s)² + 5.1m/s*14s = 385m
Thus, the final position is 385 meters from the starting point.
