The position of a particle is given by the equation where is measured in seconds and in meters (a) Find the velocity at time t (b) What is the velocity after 2 s After 4 s (c) When is the particle at rest (d) When is the particle moving forward (that is, in the positive direction) (e) Draw a diagra...

a The velocity function is the derivative of the position function b The velocity after 2 s means th ...

The position of a particle is given by the equation where is measured in seconds and in

Question:

The position of a particle is given by the equation

where is measured in seconds and in meters.

(a) Find the velocity at time t.

(b) What is the velocity after 2 s? After 4 s?

(d) When is the particle moving forward (that is, in the positive direction)?

(e) Draw a diagram to represent the motion of the particle.

(f) Find the total distance traveled by the particle during the first five seconds.

(g) Find the acceleration at time t and after 4 s.

(h) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 5.

(i) When is the particle speeding up? When is it slowing down?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

See More Books

Question Posted: Oct 31, 2023 07:10 AM

See More Questions

A particle moves according to a law of motion s = f (t), t 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second? (c) When is the...
A particle moves according to a law of motion s = f (t), t 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second? (c) When is the...
The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00m/S3)t3 - (10.0m/s2 )t2 + (9.00m/s)t. (a) Draw the x-t, v.-t, and az-f graphs of this particle. (b) At what time(s)...
In Exercises evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result. (x) = cos x, (0, 1)
Dr. Citrin had an agreement with Dr. Mehta for Mehta to work in Citrin's medical offices to see his patients when he was on vacation. While Citrin was on vacation, Mehta saw a patient and...
a. Your roommate says, Sales taxes are reported as an expense in the income statement. Do you agree? Explain. b. Jensen Company has cash proceeds from sales of $8,400. This amount includes $400 of...
Use a dot plot to display the data, which represent the blood glucose levels (in milligrams per deciliter) of 24 patients at a pathology laboratory. Organize the data using the indicated type of...
At December 31, 2008, the available-for-sale equity portfolio for Steffi Graf, Inc. is as follows. On January 20, 2009, Steffi Graf, Inc. sold security A for $15,100. The sale proceeds are net of...
How is Islamic banking different from Conventional banking? Please provide an example. Explain the main products offered by the Islamic Banks. provide some examples.
Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm 3 /s. How fast is the radius of the balloon increasing when the diameter is 50 cm?
Differentiate y = ln(x 3 + 1).
Who must obtain a preparer tax identification number?
When a certain ideal gas thermometer is dipped in water boiling at atmospheric pressure, the mercury level in the right $\mathrm{arm}$ is $1279 \mathrm{~mm}$ above the reference mark. When the...
While assembling part of an electric generator, you realize that two pieces were not properly labeled. One piece is a nonconducting block, and the other is a conducting block, but without labels you...
Find the state vector via the formal-solution approach. \(\dot{\mathbf{x}}=\left[\begin{array}{cc}0 & 1 \\ 0 & -\frac{3}{2}\end{array} ight] \mathbf{x}+\left[\begin{array}{l}0 \\ 1\end{array} ight]...
In a simplistic model of the hydrogen atom, the electron orbits the proton in a circle of radius $53 \mathrm{pm}$. What is the orbital period of the electron, in seconds, if the force responsible...
Some firms products are so well known that the entire category of products offered in the industry (including rivals products) is often referred to by the leading firms brand name (which is called an...
Discuss the benefits of a global spreadsheet identification system.
Why do markets typically lead to an efficient outcome for buyers and sellers?
Determine the domain of the function and prove that it is continuous on its domain using the Laws of Continuity and the facts quoted in this section. 35. f(x) = 2 sin x + 3 cos x 37. f(x) = x sin x
Are the following true or false? If false, state a correct version. (a) f (x) is continuous at x = a if the left- and right-hand limits of f (x) as x a exist and are equal. (b) f (x) is continuous...
In Figure 16, determine the one-sided limits at the points of discontinuity. Which discontinuity is removable and how should f be redefined to make it continuous at this point? -2 FIGURE 16
Consider the van der Waals model for a non-ideal gas. The improved model approximates the behavior of real fluids by considering the intermolecular attraction force between molecules (factor a) and...
0 (b) (c) (d) simplify the following expressions. O(n) + O(logn) + O(nlogn) O(2) O(n) 420 (n log n) +180(n) O(n) + O(m)
1. Write the right-hand side equation for the following terms: (a) p(s',rlsa) Pr (???) (b) R(sa) = E [???] (c) (sa) = Pr (???) (d) * = argmax ??? (e) V(s) = ??? (f) Q(s,a) = ???

The position of a particle is given by the equation where is measured in seconds and in

Question:

s = f(t) = t³ - 6t² +9t

Step by Step Answer:

a The velocity function is the derivative of the position function b The velocity after 2 s means th...View the full answer

Calculus

Students also viewed these Mathematics questions