An object with a known charge is first brought close to the ball so as to induce the opposite charge. Lets say we brought a positive object, so the ball will be negatively charged. Afterwards, the object with the unknown charge is brought closer. If the ball is attracted, then the object is positively charged and if it is repelled then the object is negatively charged.
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The displacement vector (SI units) is
![\vec{r} =At\hat{i}+A[t^{3}-6t^{2}]\hat{j}](https://tex.z-dn.net/?f=%5Cvec%7Br%7D%20%3DAt%5Chat%7Bi%7D%2BA%5Bt%5E%7B3%7D-6t%5E%7B2%7D%5D%5Chat%7Bj%7D)
The speed is a scalar quantity. Its magnitude is

Answer: At√(t⁴ - 12t³ + 36t² + 1)