Saturday, June 4, 2011

A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. At the bottom of the slope,...

Acceleration is defined as the rate of change of velocity. In other words,


a =  dv/dt


where a is the acceleration, dv is the change in velocity and dt is the change in time. This can also be simply written as:


acceleration = (final velocity - initial velocity) / (final time - initial time)


In this case, the final velocity = 22 m/s and the initial velocity of the roller coaster is 4 m/s. 


However, no time interval is given. Assuming that it takes the roller coaster 3 seconds to get to the final velocity, the time interval = 3 s.


Thus, average acceleration = (22 m/s - 4 m/s) / 3 s


= (18 m/s) / 3 s


= 6 m/s^2.


Thus, the roller coaster ride has an average acceleration of 6 m/s^2 over the given time duration.


Hope this helps. 

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