At time t=0 , a particle leaves the origin and moves in the positive direction of the X -axis. If the velocity of the particles varies as v (t)= v ₀ (1- t t₀ ), | v ₀ |=10 ~m / s and t₀=10 ~s , then the distance covered by the particle during the first 20 ~s is

Step-by-step solution

Given that, At t=0, x=0 and u= v =- v ₀ At any time t , velocity of particle, v = v ₀ (1- t t₀ )= v ₀- v ₀ t₀ t Velocity will become zero at time t₁ array ll & 0= v ₀- v ₀ t₀ t₁ & t₁= v ₀ v ₀ t₀=t₀=10 ~s array For time interval from 0 to 10 ~s , Acceleration, a ₁=- v ₀ t₀ =- 10 10 =-1 ~m / s ^2 and for time interval from 10 to 20 ~s Acceleration, a ₂= v ₀ t₀ =1 ~m / s ^2 Now, displacement in time 0 to 10 ~s aligned s ₁= u t₁+ 1 2 a ₁ t₁^2 & = v ₀(10)- 1 2 1(10)^2 & =10 10-50=50 ~m aligned and displacement for time