A vehicle starts moving in a straight line with an acceleration, a=4 ~m / s ^2 , with initial velocity equal to zero. After accelerating for time t₁ , the vehicle moves uniformly and for time t₂ , the vehicle finally decelerates for time t₁ eventually coming to a stop. The total time taken during the motion is 10 ~s and the average velocity during the motion is 5.1 ~m / s . The time taken by the vehicle during accele

Step-by-step solution

For first part of journey, x=0, a=4 ~ms ⁻² , time =t₁ . Velocity attained by particle at end of time t₁ is v₁=u+a t₁=4 t₁ Displacement in first t₁ seconds is s₁= 1 2 a t₁^2= 1 2 4 t₁^2=2 t₁^2 For second part of journey, initial velocity, v₁=4 t₁ , time =t₂ and acceleration =0 . Displacement in next t₂ seconds is s₂=v₁ t₂=4 t₁ t₂ For third part of journey, Initial velocity, v₁=4 t₁ Final velocity =0 Time interval =t₁ So, acceleration = 0-4 t₁ t₁ =-4 ~ms ⁻² Displacement in third part is s₃= -16 t₁^2 -8 =2 t₁^2 ( v₂^2