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:

Answer: The final velocity of the roller coaster is 58.04$\frac{m}{s}$

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=$13\frac{m}{s}$

$a=4\frac{m}{s^{2} }$

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

$v_{f} =\sqrt{3369}$

$v_{f} =58.04 \frac{m}{s}$

Answer: The final velocity of the roller coaster is $58.04\frac{m}{s}$