Question

An object if moving according to this trajectory r=(-1+2t+t2, 3.t). What is the velocity of the object? What equation is describing the movement of the object? Is the object accelerating? How do you know?

Answer 1

Explanation:

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Calculus 1 : How to find acceleration

Study concepts, example questions & explanations for Calculus 1

Example Questions

Calculus 1 Help » Spatial Calculus » Acceleration » How to find acceleration

Find Acceleration : Example Question #1

The position vector of an object moving in a plane is given by r(t)=3t4i + 6t2j. Find its acceleration when t=1.

Possible Answers:

3i + 2j

36i + 12j

3i + 6j

6i + 2j

36i - 12j

Correct answer: 36i + 12j

Explanation:

To find acceleration at time t, we have to differentiate the position vector twice.

Differentiating the first time gives the velocity:

v(t) = r'(t) = 12t3i + 12tj

Differentiating a second time gives the accelaration:

a(t) = r''(t) = 36t2i + 12j

Plug in t=1 to solve for the final answer:

a(1) = r''(1) = 36i + 12j