Question

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.

Answer 1

We will apply the equation:2as = v² - u²v = √(2as + u²)v = √(2 x 4 x 400 + 13²)v = 58 m/s

Answer 2

Answer: The final velocity of the roller coaster is 58.04
`(m)/(s)`

Step-by-step explanation:

Kinematics of the problem:

The The roller coaster moves with uniform accelerated movement moves with uniform accelerated movement, then, We use the acceleration equation for this type of movement:

`v_(f) ^(2) =v_(i) ^(2) +2*a*d` Formula 1

`v_(f)`: final speed

`v_(i)`: initial speed=
`13(m)/(s)`

`a=4(m)/(s^(2) )`

d=distance traveled by The roller coaster =400m

Final velocity calculating:

We replace known information in the formula 1:

`v_(f) ^(2) =13^(2) +2*4*400`

`v_(f) ^(2) =169+3200`

vf2=3369

`v_(f) =√(3369)`

`v_(f) =58.04 (m)/(s)`

Answer: The final velocity of the roller coaster is
`58.04(m)/(s)`