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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

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