Mathematics: The position of a particle moving along a line is given by s(t) = 2t3 - 24t2 + 90t + 7 for t â‰¥ 0. for what values of t is the speed of the particle increasing?

39Step-by-step explanation:the first three call 3, making it 3*3, then each of them will get 3 more, making it 3+(3*3)+(3*3*3),3+9+27, 39...

The position of a particle moving along a line is

Ответ:

pandadude123

15.01.2022

Mathematics

The speed of the particle increases for

Step-by-step explanation:

Given: $s(t)=2t^{3} -24t^{2} +90t+7$

To find the speed of the particle, we need a second derivative of the equation $s(t)=2t^{3} -24t^{2} +90t+7$

Differentiating, s(t) we get,

$s'(t)=6t^{2} -48t+90$

Again differentiating s'(t) , we get,

s''(t)=12t-48

Since, we need to find at what value the speed of the particle increasing, we need to equate s''(t)=0 to find the interval at which the speed of the particle increases. Thus,

$\begin{array}{r}{s^{\prime \prime}(t)=0} \\{12 t-48=0} \\{12(t-4)=0} \\{t-4=0} \\{t=4}\end{array}$

Thus, the interval are (0,4] and $[4, \infty)$

Substituting any one value between the interval (0,4] in the equation s''(t)=12t-48

$\begin{aligned}s^{\prime \prime}(t) &=12 t-48 \\s^{\prime \prime}(1) &=12-48 \\&=-36$

The speed of the particle does not increase at the interval (0,4]

Now, substituting any one value between the interval $[4, \infty)$ in the equation s''(t)=12t-48

$\begin{aligned}s^{\prime \prime}(t) &=12 t-48 \\s^{\prime \prime}(5) &=60-48 \\&=120\end{aligned}$

Thus, the speed of the particle increases during the interval $[4, \infty)$

Hence, the speed of the particle increases for

0,0(0 оценок)

The position of a particle moving along a line is given by s(t) = 2t3 - 24t2 + 90t + 7 for t â‰¥ 0. for what values of t is the speed of the particle increasing?

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question