Question

The position vector of a particle is given by r=3t^2i+4t^2j+7k find the displacement after 10s

Answer 1

r=3t^2i+4t^2j+7k
t=10 then put value of t in above equation
r=3×10×2i+4×10×2j+7k
r= 60i+80j+7k
r=under root 60^2+80^2+7^2
r=3600+6400+49=100.24

Answer 2

The displacement of the particle after 10 second has a magnitude of 500 meters.

Explanation:

Given that,

The position vector of a particle is given by :

$r=(3t^2i+4t^2j+7k)\ m$

We need to find the displacement of that particle after 10 second. It can be calculated simply putting the value of t = 10 s in above equation as :

$r=(3(10)^2i+4(10)^2j+7k)\ m$

$r=(300i+400j+7k)\ m$

Magnitude of displacement,

$|r|=\sqrt{300^2+400^2+7^2}$

|r| = 500 meters

So, the displacement of the particle after 10 second has a magnitude of 500 meters.

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