The velocity when function p(t)=11 is 8 .
According to the question
The position of a car at time t represented by function :
[tex]p(t)=t^{2} +2t-4[/tex]
Now,
When function p(t) = 11 , t will be
[tex]p(t)=t^{2} +2t-4[/tex]
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 = [tex]\frac{position}{time}[/tex]
therefore to get the value of velocity from function p(t)
we have to differentiate the function with respect to time
[tex]\frac{d(p(t))}{dt} =\frac{d}{dt} (t^{2} +2t-4)[/tex]
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:
https://brainly.com/question/12431044
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