So I have this question:

if v(t) is 2sin(e^(t/4)) + 1 and a(t) = 1/2 e^(t/4)cost(e^(t/4)) and x(0) is 2 but x(t) is uknown, is the speed of the particle increasing or decreasing at t = 5.5?

Question

So I have this question: 

if v(t) is 2sin(e^(t/4)) + 1 and a(t) = 1/2 e^(t/4)cost(e^(t/4)) and x(0) is 2 but x(t) is uknown, is the speed of the particle increasing or decreasing at t = 5.5?

anonymous · Answer

oh yea, its moving only on x axis

anonymous · Answer

idk

anonymous · Answer

So the question asks about the change in speed of the particle. This is the same as acceleration

anonymous · Answer

They're asking if acceleration is positive or negative at t=5.5

anonymous · Answer

To do this plug in 5.5 into the acceleration equation, like so:
$$a(5.5) = 1/2e^{5.5/4}\cos (e ^{\frac{ 5.5 }{ 4 }})$$

anonymous · Answer

You don't even have to know the exact acceleration, just see if it's bigger or smaller than 0, because that's all they're asking.

anonymous · Answer

$$e ^{5.5/4} > 0$$, actually, you need to know that for the cosine. it's 3.955. 
Cosine of that's -0.68

anonymous · Answer

so + * + * - is negative. So it's speed is decreasing.

anonymous · Answer

Wow, ok. Can you help with b?

 Find the average velocity of the particle for the time period 0 6.

anonymous · Answer

mmm

anonymous · Answer

Normally to find average velocity you do x(final) - x(initial) all divided by time. 
But without constant acceleration finding x(final) is difficult. 

Another method is to integrate the velocity over the time and divide by time. The integral of the velocity is going to be the distance traveled. (velocity is defined change in distance/change in time, so the time integral will just be change in distance). You can divide this by the time to get the total change in distance.

I'm not sure how to integrate the velocity here though. Best of luck :/

anonymous · Answer

Anybody know?