Question

The position of an object at time t is given by: r(t)=e^−t i + e^t j...

The position of an object at time t is given by: r(t)=e^−t i + e^t j − t√2 k, 0≤ t<∞. (a) Determine the velocity v and the speed of the object at time t. (b) Determine the acceleration of the object at time t. (c) Find the distance that the object travels during the time interval 0≤ t<ln3. Answers: (a) = velocity: v =−e^−t i + e^t j − √2 k; speed: ||v||= e^t + e^−t, (b) = acceleration: a = e^−t i + e^t j, (c) = 8/3

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The position of a particle for t > 0 is given by →r (t) = (3.0t...
The position of a particle for t > 0 is given by →r (t) = (3.0t 2 i ^ − 7.0t 3 j ^ − 5.0t −2 k ^ ) m. (a) What is the velocity as a function of time? (b) What is the acceleration as a function of time? (c) What is the particle’s velocity at t = 2.0 s? (d) What is its speed at t = 1.0 s and t = 3.0 s? (e) What is...
An object falls from rest. Its position at time t is given by s(t) = 1/2...
An object falls from rest. Its position at time t is given by s(t) = 1/2 gt^2. We consider that it falls for T seconds. (a) Write its velocity v as a function of time t and then write the velocity as a function of the position s. (b) Notice that v(T) denotes the nal velocity of the object. Write the average velocity v over the object during its fall, rst averaging over time t, and then averaging over position...
Given that the acceleration vector is a(t)=(-9 cos(3t))i+(-9 sin(3t))j+(-5t)k, the initial velocity is v(0)=i+k, and the...
Given that the acceleration vector is a(t)=(-9 cos(3t))i+(-9 sin(3t))j+(-5t)k, the initial velocity is v(0)=i+k, and the initial position vector is r(0)=i+j+k, compute: A. The velocity vector v(t) B. The position vector r(t)
Find the velocity and position vectors of a particle that has the given acceleration and the...
Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 6t j + 12t2 k, v(0) = i, r(0) = 3 j − 6 k
Find the velocity, acceleration, and speed of a particle with the given position function. (a) r(t)...
Find the velocity, acceleration, and speed of a particle with the given position function. (a) r(t) = e^t cos(t)i+e^t sin(t)j+ te^tk, t = 0 (b) r(t) = 〈t^5 ,sin(t)+ t ^ cos(t),cos(t)+ t^2 sin(t)〉, t = 1
A moving particle starts at an initial position r(0) = <1, 0, 0> with initial velocity...
A moving particle starts at an initial position r(0) = <1, 0, 0> with initial velocity v(0) = i - j + k. Its acceleration is a(t) = 4t i + 4t j + k. Find its velocity, v(t), and position, r(t), at time t.
A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2...
A particle moves with position r(t) = x(t) i + y(t) j where x(t) = 10t2 and y(t) = -3t + 2, with x and y in meters and t in seconds. (a) Find the average velocity for the time interval from 1.00 s to 3.00 s. (b) Find the instantaneous velocity at t = 1.00 s. (c) Find the average acceleration from 1.00 s to 3.00 s. (d) Find the instantaneous acceleration at t = 1.00 s.
A thrown object follows a path where at time t the position of the object is...
A thrown object follows a path where at time t the position of the object is given by r(t) = (3 + 90.63t)i + (−4.9t^2 + 42.26t + 5)j (a) What (x, y) point best descries the objects initial position? (b) If the initial velocity of the object was 100 m/s then what was the initial angle with respect to the positive horizontal axis? (c) What was the maximum height of the object?
Consider the parameterized motion given by r(t)=3t^2i-2t^2j+(6-t^3)k. Where is the object at time t=1? What is...
Consider the parameterized motion given by r(t)=3t^2i-2t^2j+(6-t^3)k. Where is the object at time t=1? What is the velocity at t=1? What is the speed at t=1? How far does the object move from 0≤t≤1? Round your answer to 2 decimal places. * r, i, j, and k should all have vector arrows above them
If the acceleration of a particle is given by a(t)=2t-1 and the velocity and position at...
If the acceleration of a particle is given by a(t)=2t-1 and the velocity and position at time t=0 are v(0)=0 and S(0)=2. 1. Find a formula for the velocity v(t) at time t. 2. Find a formula for the position S(t) at time t. 3. Find the total distance traveled by the particle on the interval [0,3].
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT