Question

The position of a car at time t is given by the function p(t)=t2 2t−4. What is the velocity when p(t)=11? assume t≥0

Answer 1

The velocity when function p(t)=11 is 8 .

According to the question

The position of a car at time t  represented by function :

$p(t)=t^{2} +2t-4$

Now,

When  function p(t) = 11 , t will be

$p(t)=t^{2} +2t-4$

11 = t²+2t-4

0 = t² + 2t - 15

or

t² +2t-15 = 0

t² +(5-3)t-15 = 0

t² +5t-3t-15 = 0

t(t+5)-3(t+5) = 0

(t-3)(t+5) = 0  

t = 3 , -5  

as t cannot be -ve as given ( t≥0)

so,

t = 3

Now,

the velocity when p(t)=11

As we know velocity = $\frac{position}{time}$

therefore to get the value of velocity from  function p(t)

we have to differentiate the function with respect to time

$\frac{d(p(t))}{dt} =\frac{d}{dt} (t^{2} +2t-4)$

v(t) = 2t + 2  

where v(t) = velocity at that time

as t = 3 for  p(t)=11  

so ,

v(t) = 2t + 2  

v(t) = 2*3 + 2  

v(t) = 8

Hence, the velocity when function p(t)=11 is 8 .

To know  more about function here:

brainly.com/question/12431044

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