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Calculus, 2ADV C1 SM-Bank 11

A particle is moving along the `x`-axis. Its velocity `v` at time `t` is given by

`v = sqrt(20t - 2t^2)`  metres per second

Find the acceleration of the particle when  `t = 4`.

Express your answer as an exact value in its simplest form.  (3 marks)

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`sqrt3/6\ \ text(ms)^(−2)`

Show Worked Solution

`v = sqrt(20t – 2t^2)`

`alpha` `= (dv)/(dt)`
  `= 1/2 · (20t – 2t^2)^(−1/2) · (20 – 4t)`

 
`text(When)\ \ t = 4,`

`alpha` `= 1/2(20 · 4 – 2 · 4^2)^(−1/2)(20 – 16)`
  `= 2/(sqrt48)`
  `= 2/(4sqrt3) xx sqrt3/sqrt3`
  `= sqrt3/6\ \ text(ms)^(−2)`