# 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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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**.