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?

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 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

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

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.