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A particle moves with a constant acceleration along the x- axis. At t=0, the particle is at x=0 and dx/dt= +4m/s. The maximum value of x-coordinate of the particle is observed 2 seconds later. Starting from t=0 after what time will it reach its position again....?

A particle moves with a constant acceleration along the x- axis. At t=0, the particle is at x=0 and dx/dt= +4m/s. The maximum value of x-coordinate of the particle is observed 2 seconds later. Starting from t=0 after what time will it reach its position again....?

Grade:upto college level

1 Answers

Anand
19 Points
7 years ago
The particle goes at const. acceleration So,the position time relation would be quadratic. Let a be the acceleration of the body .Hence the velocity would be at+c ---[1](integrating) Given At t=0 velocity is 4 m/s So c=4.The max. value of x co-ordinate is at t=2 =>dx/dt=0 at t=2 =>2a+4=0=>a= -2 m/s.s Integrating [1] x=(at^(a+1))/a+1 + 4t (Here c=0 as x=0 when t=0) =>x=2t^-1 +4t max valuues is at t=2==> x=9 Solve the quadratic eqn on t and we get soln as 2(which was given) and 0.25s

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