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Kinematics

Quick questions on Kinematics using calculus explained: O-Level A-Maths

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is integrating up the chain?
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Reversing the arrows, integration recovers velocity from acceleration and displacement from velocity:
What are using initial conditions?
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The constant is fixed by a known value, usually at t=0t = 0: an initial velocity gives the constant in the velocity expression, and an initial displacement gives the constant in the displacement expression. Find each constant before using the expression further.
What are not using the initial conditions?
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The constants come from given values at t=0t = 0 (or another stated time); leaving them as letters is incomplete.
What is sign of velocity overlooked?
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Check whether vv changes sign before computing total distance, or the parts will cancel.
What is q1?
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Given s=t3ts = t^3 - t, find the acceleration. [2 marks]
What is q2?
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A particle has a=6ta = 6t and starts from rest. Find its velocity. [3 marks]
What is q3?
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A particle has v=2t+1v = 2t + 1 and is at s=4s = 4 when t=0t = 0. Find ss. [3 marks]

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