Question

A particle moves along the x-axis so that its velocity at any time t > 0 is given by v(t)=(2π − 5)t −sin(πt) .


A. Find the acceleration at any time t.

Answer 1

the acceleration is the rate of change of velocity,
so acceleration is the derivative of velocity\[a=\frac{dv}{dt}=(2\pi -5)-\pi \cos \pi t\]

Answer 2

B. Find the minimum acceleration of the particle over the interval [0, 3]. (12 points)
So to answer B, I make the derivative = 0?

Answer 3

to find the minimum acceleration of the particle, looking at
0≤t≤3 see that when t =0, the acceleration is at a minimum.
so substitute t=0 in the equation of a

Answer 4

Thanks, for C would I substitute 2 for t?
C. Find the maximum velocity of the particle over the interval [0, 2].

Answer 5

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