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Calculus/Velocity and Acceleration

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Question
A particle moves in a straight line. It's displacement 's' metres from a fixed point 'O' after 't' seconds is given by:  s= (0.5(t^3)-13.5t+3
Calculate it's velocity after 2 seconds.
Calculate it's acceleration after 2 seconds.
At what time is the particle momentarily at rest?
Find it's acceleration at this time.

Answer
Questioner:Frances
Country:Hamilton, Bermuda
Category:Calculus
Private:No
Subject:
Mathematics- Differentiation

Question:
A particle moves in a straight line. It's displacement 's' metres from a fixed point 'O' after 't' seconds is given by:  s= (0.5(t^3)-13.5t+3
Calculate it's velocity after 2 seconds.  << "its" takes no apostrophe here
Calculate it's acceleration after 2 seconds.  << likewise
At what time is the particle momentarily at rest?
Find it's acceleration at this time.
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If s = (some function of 't'), then
v(t) = ds/dt = (the derivative of s), and
a(t) = dv/dt (the second derivative of s)

Then your questions become:

Calculate its velocity AT t = 2, meaning find v(2)
Calculate its acceleration AT t = 2, meaning find a(2)
Find t0 such that  v(t0) = 0, meaning: Set v(t0) = 0 and solve for t.
Find a(t0)

Calculus

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All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

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