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

Question

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 (A) 1 m/s (B)  3√2 m/s  (C)  5√2 m/s  (D)  7√2 m/s

Tardigrade Admin · Accepted Answer

Given, r1(t)=3 t i+4 t2 j ∴ (d r1/d t)=3 i+8 t j At t=1 s v1=(d r1/d t)=3 i+8 j Again, r2(t)=4 t2 i+3 t j (d r2/d t)=8 t i+3 j At t=1 s v2=(d r2/d t)=8 i+3 j Relative velocity =v1-v2=-5 i=5 j =√(5)2+(5)2=5 √2 m / s

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

$1 m / s$

$32 m / s$

$52 m / s$

$72 m / s$

Q. Let r1​(t)=3ti+4t2j and r2​(t)=4t2i+3rj 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=1s, will be

1m/s

32​m/s

52​m/s

72​m/s

Given, r1​(t)=3ti+4t2j ∴dtdr1​​=3i+8tj At t=1sv1​=dtdr1​​=3i+8j Again, r2​(t)=4t2i+3tjdtdr2​​=8ti+3j At t=1sv2​=dtdr2​​=8i+3j Relative velocity =v1​−v2​=−5i=5j =(5)2+(5)2​=52​m/s

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

$1 m / s$

$32 m / s$

$52 m / s$

$72 m / s$