1. Tardigrade
  2. Question
  3. Physics
  4. Let r1(t)=3 t i+4 t2 j and r2(t)=4 t2 i+3 r j represent the positions of particles 1 and 2 , respectively, as function of time t, r1(t) and r2(t) are in meter and t in second. The relative speed of the two particles at the instant t =1 s, will be

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Q. Let $r_{1}(t)=3 t i+4 t^{2} j$ and $r_{2}(t)=4 t^{2} i+3 r j$ represent the positions of particles $1$ and $2$ , respectively, as function of time $t, r_{1}(t)$ and $r_{2}(t)$ are in meter and $t$ in second. The relative speed of the two particles at the instant $t =1\, s$, will be

AMUAMU 2012

Solution:

Given, $r_{1}(t)=3 t i+4 t^{2} j$
$\therefore \frac{d r_{1}}{d t}=3 i+8 t j$
At $t=1 s v_{1}=\frac{d r_{1}}{d t}=3 i+8 j$ Again,
$r_{2}(t)=4 t^{2} i+3 t j \frac{d r_{2}}{d t}=8 t i+3 j$
At $t=1 s v_{2}=\frac{d r_{2}}{d t}=8 i+3 j$
Relative velocity $=v_{1}-v_{2}=-5 i=5 j$
$=\sqrt{(5)^{2}+(5)^{2}}=5 \sqrt{2}\, m / s$