The position of a particle P moving in the horizontal plane is described by r(t)=(5t2i + 4te0.1tj) m. Find the magnitude of the velocity at t=2 seconds. Specify your answer in m/s to 1 decimal place Solution velocity is given by dr/dt r(t)=(5t2i+ 4te0.1tj) m dr/dt = 10t i + (0.4te0.1t + 4e0.1t) m/s at t = 2 seconds , then , v = ( 20 i + 5.87 j ) m/s magnitude of velocity = sqrt(20^2 + 5.87^2) magnitude of velocity = 20.8 m/s magnitude of the velocity at t=2 seconds is 20.8 m/s.

1. The position of a particle P moving in the horizontal plane is described by r(t)=(5t2i + 4te0.1tj)
m. Find the magnitude of the velocity at t=2 seconds. Specify your answer in m/s to 1 decimal
place
Solution
velocity is given by dr/dt
r(t)=(5t2i+ 4te0.1tj) m
dr/dt = 10t i + (0.4te0.1t + 4e0.1t) m/s
at t = 2 seconds ,
then ,
v = ( 20 i + 5.87 j ) m/s
magnitude of velocity = sqrt(20^2 + 5.87^2)
magnitude of velocity = 20.8 m/s
magnitude of the velocity at t=2 seconds is 20.8 m/s