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How do I use Integrals to find how Velocity is behaving given the Acceleration?
I am given the following :
s(0) = 0 ft
V(0) = 70 ft/s
The following points on the graph a(t) in ft/sec² :
(2, -4), (10, -8), (14, -4), (18,15), (20, 15)
Is the velocity of the car increasing, decreasing, or constant at t = 10, 14 & 19secs?
I know this is a lot of work, but please help in any way possible. I'm really desperate for it.
Also could you tell me how to find the Minimum and Maximum Velocity and when it occurs?
EDIT : I JUST NOTICED SOMETHING :
The graph is a(t), so is it technically a graph of velocity because acceleration * time = velocity?
2 Answers
- Anonymous8 years agoFavorite Answer
orrrrrrr you could
1) find the function for a(t)
2) integrate the function of a(t) to get the function for v(t)
- 8 years ago
Are you given a graph and just specified the turning points?
At t=10, a=-8, so velocity is decreasing. At t=14, a=-4, so velocity is decreasing. At t=19, acceleration is probably around 15, so velocity is increasing.
The second part uses integrals. Estimate the area under the acceleration graph from t=0. When a<0, area is decreasing. The minimum and maximum velocity will happen when acceleration is zero. The minimum will be when the area is lowest and the maximum is when the area is highest. Add 70 to the areas to find the values at the mins and maxs.
Source(s): Physics class