Acceleration of Kingda Ka

For the first lab in the physics class, we did the sugar pack lab, which measures the acceleration of the little car. In the lab, we use the time and the distance of the car traveled to calculate the acceleration. Basically, we put our data(distance and time) into the plot and draw a best-fitted line to get the acceleration. On the second part of the lab, we used the distance and the time to calculate the velocity and eventually get the deceleration of the little car. 


In the lab the equations we used are:

• Average velocity = delta distance/delta time
• distance  = velocity * time
• Average acceleration = delta velocity/time
• velocity final = velocity + acceleration *time

 I think we can also utilize these equations in our real life besides the lab, for example, ROLLER COASTERS.

The roller coasters always give people exciting feeling by their fast speed. Usually, the acceleration of the roller coasters is high because it needs short time and short distance for reaching its maximum speed, but how high does it usually is?

Let's use the example of the Kingda Ka, the tallest and the second fastest of roller coasters in the world. 

According to the official data, the train can reach 128 miles per hour (206 km/h) in 3.5 seconds. 

Now we knew the V final is 206km/h, which equals to 57.2m/s. We can assume the V initial is 7m/s because the start of the roller coaster is kind of slow; 7m/s is probably a little bit faster than the average human walking speed. The time we use is 3.5 second. 

According to the equation V final = V initial + accleration * time:

57.2m/s = 7m/s + a * 3.5

then we can get the acceleration of Kingda Ka is about 14m/s^2.