Question Video: Finding the Displacement of a Particle Based on Time and the Position Vector of the Particle | Nagwa Question Video: Finding the Displacement of a Particle Based on Time and the Position Vector of the Particle | Nagwa

# Question Video: Finding the Displacement of a Particle Based on Time and the Position Vector of the Particle Mathematics

The position vector of a particle relative to the point π is given by the relation π« = (π‘Β² + 4π‘ β 5)π’, where π’ is a fixed unit vector and π‘ is the time. Find the displacement of the particle after 3 seconds.

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### Video Transcript

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. Find the displacement of the particle after three seconds.

The displacement of a particle is the change in position. This is measured from the origin or start point. Therefore, the displacement of the particle after three seconds will be equal to π« of three minus π« of zero. When π‘ is equal to three, π« is equal to three squared plus four multiplied by three minus five π’. Three squared is equal to nine. Four multiplied by three is 12. So we have nine plus 12 minus five π’. Nine plus 12 is equal to 21, and subtracting five gives us 16π’.

When π‘ is equal to zero, we have zero squared plus four multiplied by zero minus five π’. Both zero squared and four multiplied by zero are equal to zero. This means weβre left with negative five π’. We need to subtract this from 16π’. This is the same as adding five π’ to 16π’. The displacement of the particle after three seconds is therefore equal to 21π’.