In physical science, there is an equation that relates the distance, initial velocity, final velocity and acceleration. This equation is written below.
d = (Vf² - Vi²) / 2a
where d is the distance,
Vf is the final velocity,
Vi is the initial velocity, and
a is the acceleration
To get the value of Vf we may rearrange the equation such that,
Vf² - Vi² = 2ad
Transposing Vi² to the other side of the equation,
Vf² = 2ad + Vi²
Then, we get the square root of each side,
Vf = sqrt (2ad + Vi²)
Substitute the given values above,
Vf = sqrt ((2)(4 m/s²)(400 m) + (13 m/s)²)
Vf = 58.04 m/s
Hence, the final velocity of the roller coaster is approximately 58.04 m/s.
