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 moves along the x-axis so that at time t >= 0 its velocity is given by v(t)=3t^(2)-28 t+25. Determine the speed of the particle at t=9. Answer:

A particle moves along the x x -axis so that at time t≥0 t \geq 0 its velocity is given by v(t)=3t2−28t+25 v(t)=3 t^{2}-28 t+25 . Determine the speed of the particle at t=9 t=9 .\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 moves along the x x -axis so that at time t≥0 t \geq 0 its velocity is given by v(t)=3t2−28t+25 v(t)=3 t^{2}-28 t+25 . Determine the speed of the particle at t=9 t=9 .\newlineAnswer:
  1. Identify Given Velocity Function: Identify the given velocity function and the time at which we need to find the speed.\newlineThe velocity function is v(t)=3t2−28t+25v(t)=3t^{2}-28t+25, and we need to find the speed at t=9t=9.
  2. Plug in Value of t: Plug the value of tt into the velocity function to find the velocity at t=9t=9. \newlinev(9)=3(9)2−28(9)+25v(9)=3(9)^{2}-28(9)+25
  3. Calculate Velocity at t=9t=9: Calculate the velocity at t=9t=9.v(9)=3(81)−28(9)+25v(9)=3(81)-28(9)+25v(9)=243−252+25v(9)=243-252+25
  4. Finish Velocity Calculation: Finish the calculation of the velocity at t=9t=9.v(9)=243−252+25v(9)=243-252+25v(9)=−9+25v(9)=-9+25v(9)=16v(9)=16
  5. Calculate Speed at t=9t=9: Since speed is the absolute value of velocity, calculate the speed at t=9t=9.
    Speed at t=9t=9 = ∣v(9)∣|v(9)|
    Speed at t=9t=9 = ∣16∣|16|
  6. Conclude Final Speed: Conclude with the final value of the speed at t=9t=9.\newlineSpeed at t=9t=9 = 1616 (since 1616 is already positive, its absolute value is also 1616)

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 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:
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

View all (107)

Related topics

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