The position vector of a particle is determined by the expression r → = 2 t 2 i ^ + 3 t j ^ + 9 k ^ . The magnitude of its displacement (in m ) in first two seconds is

r → = 2 t 2 i ^ + 3 t j ^ + 9 k ^ At t = 0 , r 1 → = 9 k ^ At t = 2 s , r 2 → = 8 i ^ + 6 j ^ + 9 k ^ ∴ Δ r → = r 2 → - r 1 → = 8 i ^ + 6 j ^ ∴ Δ r → = r 2 → - r 1 → = 8 2 + 6 2 = 10 m

Physics - Kinematics Question with Solution | TestHub

PhysicsKinematics1-DEasy2 minPYQ_2020

PhysicsEasynumerical

The position vector of a particle is determined by the expression $\vec{r} = 2 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k}$ . The magnitude of its displacement (in $m$ ) in first two seconds is

Answer:

10.00

Solution:

$\vec{r} = 2 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k}$
At $t = 0, \vec{r_{1}} = 9 \hat{k}$
At $t = 2 s, \vec{r_{2}} = 8 \hat{i} + 6 \hat{j} + 9 \hat{k}$
$∴ Δ \vec{r} = \vec{r_{2}} - \vec{r_{1}} = 8 \hat{i} + 6 \hat{j}$
$∴ |Δ \vec{r}| = |\vec{r_{2}} - \vec{r_{1}}| = \sqrt{{(8)}^{2} + {(6)}^{2}} = 10 m$

Subject:PhysicsTopic:KinematicsSubtopic:1-D

⏱ 2mℹ️ Source: PYQ_2020

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