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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.

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

Answers by Expert:

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.

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.**Education/Credentials**

(See above.)