Question

A new roller coaster opened at Cedar Point. The coaster has a top velocity of 149 mi/h and accelerates at a rate of 30.4 mi/h/s in a time of 4.90 s. What is the roller

coasters initial velocity?
mi/h

Answer 1

The initial velocity of the roller coaster is approximately 0.04 mi/h, which is calculated using the final velocity, acceleration, and the time during which the acceleration occurs.

Step-by-step explanation:

The question asks for the roller coaster's initial velocity given a top velocity, acceleration rate, and the time over which this acceleration occurs. To find the initial velocity, we can use one of the kinematic equations of motion:

v = u + at

In this equation, v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We can rearrange this to solve for the initial velocity:

u = v - at

Using the values given:

• Final velocity, v = 149 mi/h
• Acceleration, a = 30.4 mi/h/s
• Time, t = 4.90 s

u = 149 mi/h - (30.4 mi/h/s × 4.90 s)

u = 149 mi/h - 148.96 mi/h

u = 0.04 mi/h

The roller coaster's initial velocity is approximately 0.04 mi/h, which is close to being from rest.