The position vector of a particle is determined by the expression overset arrow r=2t2 hati+3t hatj+9 hatk , where t represents time in seconds. The magnitude of its displacement (in m ) in first two seconds is

Question

The position vector of a particle is determined by the expression overset arrow r=2t2 hati+3t hatj+9 hatk , where t represents time in seconds. The magnitude of its displacement (in m ) in first two seconds is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

overset arrow r=2t2 hati+3t hatj+9 hatk At t=0, overset arrow r1=9 hatk At textt=2 texts, overset arrow textr2=8 hat texti+6 hat textj+9 hat textk ∴ Δ overset arrow textr= overset arrow textr2- overset arrow textr1=8 hat texti+6 hat textj ∴|Δ rr|=|r2-r1|=√(8)2+(6)2=10 m

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

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

Q. The position vector of a particle is determined by the expression r→=2t2i^+3tj^​+9k^ , where t represents time in seconds. The magnitude of its displacement (in m ) in first two seconds is

r→=2t2i^+3tj^​+9k^ At t=0,r1​→​=9k^ At t=2s,r2​→​=8i^+6j^​+9k^ ∴Δr→=r2​→​−r1​→​=8i^+6j^​ ∴∣∣​Δrr​​∣∣​=∣∣​r2​​−r1​​∣∣​=(8)2+(6)2​=10m

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

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