Calculating Final Velocity

A roller coaster is traveling at 13 m/s when it approaches a hill that is 400 m long. Heading down the hill, it accelerates at 4.0 m/s2. What is the final velocity of the roller coaster? Round your answer to the nearest whole number.

m/s

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.