A particle moves along the x-axis with x(t)=10+8t-3t². Another particle moves along the y-axis with y(t)=5-8t³. At t=1 s, the speed of the second particle as measured in the frame of the first is √ν. Find ν.
Physics · Kinematics part-3 Relative motion · Relative motion in one dimension
JEE Mains

Question

A particle moves along the x-axis with x(t)=10+8t-3t². Another particle moves along the y-axis with y(t)=5-8t³. At t=1 s, the speed of the second particle as measured in the frame of the first is √ν. Find ν.

Physics · Kinematics part-3 Relative motion · Relative motion in one dimension

G1 Physics · Accepted Answer

At t=1 s, first-particle velocity is v₁=(dx/dt)î=(8-6t)î=2î m s⁻¹. Second-particle velocity is v₂=(dy/dt)ĵ=-24t²ĵ=-24ĵ m s⁻¹. Relative velocity v₂₁=v₂-v₁=-2î-24ĵ. Relative speed squared=2²+24²=580. Therefore ν=580.