8. Exercises

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Exercise 8.1


The acceleration of a jet-ski is (\displaystyle 0.9\mathbf{i}+0.7\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-2}}. Its initial velocity is 4\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}} and its initial position is (\displaystyle 400\mathbf{i}+350\mathbf{j}) m. The unit vectors are directed east and north respectively.

a) Find the velocity of the jet-ski when t = 10 seconds.

b) Find the position of the jet-ski when t = 10 seconds.



Exercise 8.2


A particle is set into motion on a smooth inclined plane. The initial velocity of the particle is 5\displaystyle \mathbf{i} \displaystyle \text{m}{{\text{s}}^{-1}}, its acceleration is -4\displaystyle \mathbf{j} \displaystyle \text{m}{{\text{s}}^{-2}} and its initial position is (\displaystyle 18\mathbf{i}+14\mathbf{j}) m, where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular unit vectors that lie in the plane in which the particle is moving.

a) Find the velocity of the particle after it has been moving for 4 seconds.

b) Find the position of the particle after it has been moving for 8 seconds.