Question

Position vector of a particle is given by r= 6ti+8tj+5k, find the displacement after 10 seconds.

Answer 1

The position of the particle is given as a function of time. So, we just need to calculate the position vector of the particle at time t=0 and t=10 s and take the difference between them to find its displacement.

r(t)=6ti+8tj+5k

r(0)= 5k
r(10)= 60i+80j+5k

Now, the displacement after 10sec =
r(10)-r(0)=(60i+80j+5k) - 5k

Displacement vector = ( 60i +80j ) units

Magnitude of displacement =√(60²+80²)
=√100² = 100m

Hope you understand the concept.
All the best!