Equation of motion of a body moving along x-axis at an instant t seconds is a given by X is equals to 40 + 20t - t3 Cube .displacement of the particle come before coming to rest is
Answers
Explanation:
At t=0 , particle is at , let`s say x distance ,from O ;then putting t=0 in the given displacement-time equation we get;x =40 +12(0) -(0)³ = 40 m ___________________Particle comes to rest that means velocity of particle becomes zero after travelling certain displacement ; let`s say the time be t.then after differentiating the given displacement-time equation wrt time we get velocity-time equation -->v= 12-3t²at time t =t (the time when the particle comes to rest ):v= 0;=> 12-3t² = 0;=> t = 2 s _____________________Then ,at t =2s we are at , let`s say x` distance from O ;put this value of t (=2) in given displacement-time equation , we get;x`= 40 +12(2) -(2)³;= 56m.
Answer:
★ X = 40+12t-t³
Differencing both side :
➟ dx/dt = d(40+12t-t³)/dt
We know dx/dt = v , So
➟ v = 0 + 12 - 3t²
➟ 3t² = 12
➟ t² = 4
➟ t = 2
Pluging t=2 in Equation
➟ X = 40 + 12*2 - 2³
➟ X = 64 - 8
➟ X = 56 m