Differentiating Vectors (Leaving Cert Applied Maths): Quizzes

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Differentiating Vectors
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How do we differentiate vectors with respect to time?

Treat each component separately

What is the second step in vector differentiation?

Differentiate the iˉ\bar{i} component

What do you get when you differentiate a displacement vector?

Velocity vector

What do you get when you differentiate a velocity vector?

Acceleration vector

What is speed in relation to velocity?

The magnitude of velocity

What is the magnitude of vector 5iˉ+12jˉ5\bar{i} + 12\bar{j}?

13

Given sˉ=(3t3−1)iˉ+(100−4t3)jˉ\bar{s} = (3t^3 - 1)\bar{i} + (100 - 4t^3)\bar{j}, what is vˉ\bar{v}?

9t2iˉ−12t2jˉ9t^2\bar{i} - 12t^2\bar{j}

Given vˉ=81iˉ−108jˉ\bar{v} = 81\bar{i} - 108\bar{j}, what is the speed?

135 m/s

Given vˉ=9t2iˉ−12t2jˉ\bar{v} = 9t^2\bar{i} - 12t^2\bar{j}, what is aˉ\bar{a}?

18tiˉ−24tjˉ18t\bar{i} - 24t\bar{j}

When should you substitute time values in differentiation problems?

After differentiating

What are the correct units for velocity?

m/s

Which statement about speed is correct?

Speed is always positive

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