Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A particle travels along the x-axis such that its acceleration is given by a(t)=(t^(0.5)+3)cos(3t). If the velocity of the particle is v=-2 when t=1, what is the velocity of the particle when t=1 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

A particle travels along the x x -axis such that its acceleration is given by a(t)=(t0.5+3)cos⁡(3t) a(t)=\left(t^{0.5}+3\right) \cos (3 t) . If the velocity of the particle is v=−2 v=-2 when t=1 t=1 , what is the velocity of the particle when t=1 t=1 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Relate position, velocity, speed, and acceleration using derivativesright chevron icon

Full solution

Q. A particle travels along the x x -axis such that its acceleration is given by a(t)=(t0.5+3)cos⁡(3t) a(t)=\left(t^{0.5}+3\right) \cos (3 t) . If the velocity of the particle is v=−2 v=-2 when t=1 t=1 , what is the velocity of the particle when t=1 t=1 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
  1. Identify Given Information: Identify the given information and what is being asked.\newlineWe are given the acceleration function a(t)=(t0.5+3)cos⁡(3t)a(t) = (t^{0.5} + 3)\cos(3t) and the initial velocity v=−2v = -2 at t=1t = 1. We need to find the velocity of the particle at t=1t = 1.
  2. Recognize Initial Velocity: Recognize that the velocity at t=1t=1 is already given.\newlineThe problem states that the velocity vv is −2-2 when t=1t = 1. Since we are asked to find the velocity at the same point in time (t=1t = 1), we do not need to perform any further calculations.

More problems from Relate position, velocity, speed, and acceleration using derivatives

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t0.7sin⁡(2t+3) v(t)=t^{0.7} \sin (2 t+3) . What is the acceleration of the particle at time t=4 t=4 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t1.1cos⁡(t2−5) v(t)=t^{1.1} \cos \left(t^{2}-5\right) . If the position of the particle is x=−2 x=-2 when t=2.5 t=2.5 , what is the position of the particle when t=1 t=1 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t0.9sin⁡(t−1) v(t)=t^{0.9} \sin (t-1) . If the position of the particle is x=−3 x=-3 when t=3 t=3 , what is the position of the particle when t=5 t=5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t2.1sin⁡(2t) v(t)=t^{2.1} \sin (2 t) . Find all times when the speed of the particle is equal to 22 on the interval 0≤t≤4 0 \leq t \leq 4 . You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer: t= t=
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=(t2.3+5)sin⁡(2t) v(t)=\left(t^{2.3}+5\right) \sin (2 t) . What is the distance traveled by the particle over the interval 0≤t≤5 0 \leq t \leq 5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t1.9cos⁡(3t−1) v(t)=t^{1.9} \cos (3 t-1) . What is the distance traveled by the particle over the interval 0≤t≤3 0 \leq t \leq 3 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=(t1.6+3)cos⁡(3t) v(t)=\left(t^{1.6}+3\right) \cos (3 t) . What is the average velocity of the particle on the interval 0≤t≤6 0 \leq t \leq 6 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=t2.1sin⁡(2t+5) v(t)=t^{2.1} \sin (2 t+5) . Find all times when the speed of the particle is equal to 11 on the interval 0≤t≤3 0 \leq t \leq 3 . You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer: t= t=
Get tutor helpright-arrow

Posted 9 months ago

Question
A particle travels along the x x -axis such that its velocity is given by v(t)=(t2.1+5)cos⁡(2t) v(t)=\left(t^{2.1}+5\right) \cos (2 t) . What is the distance traveled by the particle over the interval 0≤t≤5 0 \leq t \leq 5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:
Get tutor helpright-arrow

Posted 9 months ago

Question
You pick a card at random, put it back, and then pick another card at random.\newline44\newline55\newline66\newline77\newlineWhat is the probability of picking a number greater than 55 and then picking a 44 ?\newlineWrite your answer as a percentage.
Get tutor helpright-arrow

Posted 1 month ago

View all (107)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant