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The position vector of a particle relative to the point π is given by the relation π« is equal to π‘ squared plus four π‘ minus five π’, where π’ is a fixed unit vector and π‘ is the time.
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Find the displacement of the particle after three seconds.
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The displacement of a particle is the change in position.
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This is measured from the origin or start point.
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Therefore, the displacement of the particle after three seconds will be equal to π« of three minus π« of zero.
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When π‘ is equal to three, π« is equal to three squared plus four multiplied by three minus five π’.
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Three squared is equal to nine.
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Four multiplied by three is 12.
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So we have nine plus 12 minus five π’.
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Nine plus 12 is equal to 21, and subtracting five gives us 16π’.
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When π‘ is equal to zero, we have zero squared plus four multiplied by zero minus five π’.
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Both zero squared and four multiplied by zero are equal to zero.
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This means weβre left with negative five π’.
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We need to subtract this from 16π’.
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This is the same as adding five π’ to 16π’.
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The displacement of the particle after three seconds is therefore equal to 21π’.