Answer :
The electric grinder made 1826 revolutions while slowing down to a complete stop, calculated by using the formulas for deceleration and distance under a velocity-time graph.
To calculate how many revolutions the grinder made while slowing to a stop, we first need to know the deceleration.
Since the grinder comes to a stop, its final velocity is 0 rev/s. The initial velocity is 44 rev/s and it takes 83 seconds to stop.
The deceleration can be calculated using the formula:
a = (v_f - v_i) / t
Where:
- a is the deceleration
- v_f is the final velocity, which is 0 rev/s
- v_i is the initial velocity, which is 44 rev/s
- t is the time, which is 83 seconds
The number of revolutions while slowing down is the area under the velocity-time graph, which is a triangle in this case.
So, the total revolutions (N) can be found using the formula:
N = 0.5 * (v_i + v_f) * t
Substitute the known values:
N = 0.5 * (44 rev/s + 0) * 83 s = 0.5 * 44 * 83 = 1826 revolutions.
Therefore, the grinder made 1826 revolutions while slowing down to a stop.
