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The displacement of a body from an origin O at a time t seconds is x metres where  ...

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nerdygirl-1996 | Student, Undergraduate | Honors

Posted August 24, 2013 at 3:01 PM via web

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The displacement of a body from an origin O at a time t seconds is x metres where  

`x= t^2- 11t+3`

Find the values for t  for which the body has a speed of 5 m/s. Hint: two values exost

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llltkl | College Teacher | Valedictorian

Posted August 24, 2013 at 3:40 PM (Answer #1)

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The displacement of a body from an origin O at a time t seconds is x metres where:

`x=t^2-11t+3`

Dividing both sides by t we get:

`x/t=t-11+3/t`

`x/t` is the speed,

So, speed`=t-11+3/t`

Put speed=5 m/s,

`5=t-11+3/t`

`rArr 16t=t^2+3`

`rArr t^2-16t+3=0`

From the quadratic formula,

`t=(16+-sqrt(16^2-4*1*3))/(2*1)`

=15.81025 s and 0.94875 s

Therefore, the values of t for which the body has a speed of 5 m/s are 15.81025 s and 0.94875 s.

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