Question

The speed of a roller coaster cart in Six Flags increases from 2.5 m/s to 9.0 m/s in 3.0 seconds as it accelerates uniformly down a hill. Calculate for the acceleration of the roller coaster during this 3.0 second period?

Answer 1

The roller coaster cart accelerates uniformly at 2.17 m/s² as its speed increases from 2.5 m/s to 9.0 m/s over 3.0 seconds down a hill.

Step-by-step explanation:

To calculate the acceleration of a roller coaster cart that uniformly increases its speed from 2.5 m/s to 9.0 m/s in a 3.0-second interval, we can use the formula for acceleration, which is the change in velocity divided by the time taken for the change. The change in velocity (Δv) is the final velocity (vf) minus the initial velocity (vi). For this scenario, Δv = 9.0 m/s - 2.5 m/s = 6.5 m/s. Therefore, the acceleration (a) is Δv divided by the time interval (t), which is:

a = Δv / t = 6.5 m/s / 3.0 s = 2.17 m/s2.

The roller coaster experiences an acceleration of 2.17 m/s2 during the 3.0-second period as it descends the hill.