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:

An object travels along a straight line. The function s(t)=3cos⁡t−7ets(t) = 3\cos t - 7e^t gives the object's position, in feet, at time tt seconds.\newlineWrite a function that gives the object's velocity v(t)v(t) in feet per second.\newlinev(t) = ______

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. An object travels along a straight line. The function s(t)=3cos⁡t−7ets(t) = 3\cos t - 7e^t gives the object's position, in feet, at time tt seconds.\newlineWrite a function that gives the object's velocity v(t)v(t) in feet per second.\newlinev(t) = ______
  1. Differentiate s(t)s(t): To find the velocity function v(t)v(t), we need to differentiate the position function s(t)s(t) with respect to time tt.
  2. Form v(t)v(t): Combine the derivatives to form the velocity function v(t)v(t).

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 2 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 2 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 2 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 2 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 2 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 2 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 2 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 2 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 2 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 2 months ago

View all (149)