Question

User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.

172

likes
858 views

Answer to a math question User One of the applications of the derivative of a function is its use in Physics, where a function that at every instant t associates the number s(t), this function s is called the clockwise function of the movement. By deriving the time function we obtain the velocity function at time t, denoted by v(t). A body has a time function that determines its position in meters at time t as S(t)=t.³√t+2.t . Present the speed of this body at time t = 8 s.

Expert avatar
Timmothy
4.8
98 Answers
1. Find the Velocity Function v(t): The velocity function v(t) is the derivative of the position function s(t) with respect to time t. s\left(t\right)=t^{\frac{3}{2}}+2t Applying the power rule and the derivative of a constant term, we get: v\left(t\right)=\frac{3}{2}t^{\frac{1}{2}}+2 2. Evaluate v(t) at t=8 seconds: Now, substitute t=8 into the velocity function v(t) to find the velocity at t=8 seconds: v\left(8\right)=\frac{3}{2}8^{\frac{1}{2}}+2=8 Therefore, at t=8 seconds, the velocity of the body is 8m/s.

Frequently asked questions (FAQs)
What is the derivative of cos²(3x) with respect to x?
+
How many gallons of water does a swimming pool hold if it is 20 feet long, 10 feet wide, and 5 feet deep?
+
How many different ways can you arrange the letters "MATHS" in a row?
+
New questions in Mathematics
I want to divide R$ 2200.00 between Antônio, Beto and Cássia, so that Beto receives half from Antônio and Cássia receives a third of Beto. Under these conditions, how much more will Beto receive than Cássia?
5 . {2/5 + [ (8/-9) - (1/-7) + (-2/5) ] ÷ (2/-5)} . 8/15
If you have a bag with 18 white balls and 2 black balls. What is the probability of drawing a white ball? And extracting a black one?
-6n+5=-13
-6(3x-4)=-6
Equivalent expression of the sequence (3n-4)-(n-2)
Find all real numbers x that satisfy the equation \sqrt{x^2-2}=\sqrt{3-x}
sin 30
6-35 A recent study by an environmental watchdog determined that the amount of contaminants in Minnesota lakes (in parts per million) it has a normal distribution with a mean of 64 ppm and variance of 17.6. Assume that 35 lakes are randomly selected and sampled. Find the probability that the sample average of the amount of contaminants is a) Greater than 72 ppm. b) Between 64 and 72 ppm. c) Exactly 64 ppm. d) Greater than 94 ppm.
3/9*4/8=
From 1975 through 2020 the mean annual gain of the Dow Jones Industrial Average was 652. A random sample of 34 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 800? Assume the standard deviation is 1539
X~N(2.6,1.44). find the P(X<3.1)
List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)
During a month's time, an automobile sales person receives a 6% commission on the first $5000 in sales, a 7% commission on the next $5000 sales, 8% commission on anything over $10,000. What is her commission for $36,000 in sales?
find missing measure for triangle area = 48 m square base = 10m heaighy = ? m
A buyer purchased a North Carolina home for $475,250. The seller allowed the buyer to assume his first small mortgage with a loan balance of $110,000. How much is the excise tax paid in the transaction? $951 $729.50 $950.50 $221 none of the above
Pablo has a balance of $440,000 and 2/5 of the money is used to pay bills. How much money do you have left after paying the bills?
How do you convert a fraction to a decimal
3(x-4)=156
Dano forgot his computer password. The password was four characters long. Dano remembered only three characters: 3, g, N. The last character was one of the numbers 3, 5, 7, 9. How many possible expansions are there for Dano's password?