A scienctist discovers that a particle moves with a position function given by the relation x = 2.66t^4-0.394t^3+117. Find the instantanous velocity and acceleration as a function of time, the particle's average acceleration during the time interval from t1 = 4.00s to t2=6.00s, and the instantanous acceleration at t=5.00s

Question

A scienctist discovers that a particle moves with a position function given by the relation x = 2.66t^4-0.394t^3+117.  Find the instantanous velocity and acceleration as a function of time, the particle's average acceleration during the time interval from t1 = 4.00s to t2=6.00s, and the instantanous acceleration at t=5.00s

anonymous · Answer

I've done the first two problem and I'm working on the third right now. I'll post up what I have so far...

anonymous · Answer

$$v=\frac{dv}{dt} = 10.64t^3-1.182t^2$$ (instant velocity)
$$a=\frac{dv}{dt}= 31.92t^2-2.364t$$(instant acceleration)

anonymous · Answer

This one I'm not 100% sure I'm doing correctly. I know the the average accleration is $$ave acceleration = \frac{v_{2}-v_{1}} {t_{2}-t_{1}}$$ so would I just plug in t1 and t2 into t in my fvelocity answer I got above and then plug that into the ave. acceleration formula?

asnaseer · Answer

yes - your approach is correct to find the average acceleration

anonymous · Answer

okay thanks, I'll try to get the rest of the problem done and let you know id I have any other issues. Thanks.