Question

The position of an object is describe by the vector r = t2 i + 2t j – t k at any time t. Find its position, velocity and acceleration at time t = 6s.​

Answer 1

Answer:

(4) 12î + 2j^ + k^ is your answer

Explanation:

I hope it helped you

Answer 2

The position of an object is 36 i + 12j – 6 k at time t = 6s.

The velocity of an object is 12 i + 2j – 1k at time t = 6s.

The acceleration of an object is 2i at time t = 6s.

Given:

r = t² i + 2t j – t k at any time t.

To Find:

The position, velocity, and acceleration at time t = 6s.​

Solution:

We are required to find the position, velocity, and acceleration at time t = 6s.​

It is given that r = t² i + 2t j – t k -----(1)

To find the position at t = 6s substitute the value of t in equation(1)

r = 6² i + 12 j – 6 k

r = 36 i + 12j – 6 k

Therefore, The position of an object is 36 i + 12j – 6 k at time t = 6s.

To find the velocity differentiate vector r with respect to 't'

v = 2t i + 2 j – 1 k   --------(2)

Substitute the value of t = 6 in equation(2)

v = 12 i + 2j – 1k

Therefore, The velocity of an object is 12 i + 2j – 1k at time t = 6s.

To Find the acceleration differentiate the velocity vector with respect to 't'

a = 2 i ------- (3)

There is no 't' variable in equation(3) so the acceleration vector is not dependent on time 't'.

Therefore, The acceleration of an object is 2i at time t = 6s.

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