Integration and kinematics

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nilaani09

ExamQA+ A2 Maths, A2 Chemistry, A2 Biology, LSC Queensbury

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Mar 11, 2021 9:07 pm

(@nilaani09)

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I don’t understand how to work out the average velocity on question 9?

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Posts: 770

Zeeshan Ahmed

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Mar 11, 2021 9:56 pm

(@zeeshan)

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Average velocity is the mean of the 2 velocities at t = 5 and t = 8

And remember, to go from acceleration to velocity you integrate the acceleration equation.

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nilaani09

ExamQA+ A2 Maths, A2 Chemistry, A2 Biology, LSC Queensbury

(@nilaani09)

Joined: 3 years ago

Eminent Member

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Mar 12, 2021 1:22 pm

Reply to

Zeeshan Ahmed

@zeeshan

The mark scheme says the answer is -116ms^-1 but I’m not sure what I did wrong??

Zeeshan Ahmed

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(@zeeshan)

Joined: 4 years ago

Prominent Member

Posts: 770

Mar 12, 2021 3:19 pm

Reply to

nilaani09

@nilaani09

Hmm. Yes 116 is actually correct - my mistake.

What I said would only apply if the velocity was a linear equation, e.g. v = 2 + 4t or something like that.

Since your velocity equation ended up being non linear (a quadratic), you'd have to use the fact that average velocity = total displacement / total time.

So in other words, from your new velocity equation, integrate it one more time to find the equation for displacement, then work out the total displacement between t = 5 and t = 8. (plug them into the displacement equation then minus from each other). Once you've got the total displacement between the two times, divide by total time taken (8 - 5 = 3 seconds). You should end up with 116.

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