A roller coaster is moving at 25 m/sec at the bottom of a hill. Three seconds later it reaches the top of the next hill, moving at 10m/sec. What is the acceleration? Is it increasing or decreasing its speed?
The acceleration of an object is the rate of change of its velocity. Mathematically it is given as:
a = dv/dt
where a is the acceleration, V is velocity and t is the time. This can also be given as,
a = (v2 - v1)/t
where v2 and v1 are velocities at two different times and t is the time duration between instance 1 and 2.
In this case, the velocity of the roller coaster changes from 25 m/sec to 10 m/sec in a duration of 3 sec. Hence, the acceleration of the roller coaster can be calculated as:
a = (10 -25)/3 = -15/3 = -5 m/s^2
Since, the velocity is decreasing, the roller coaster is decelerating ( and hence the negative sign) at a rate of 5 m/s^2.
The roller coaster may again accelerate as it moves from top of the hill to bottom of the hill.
Hope this helps.