A body of mass m moves along X-axis such that its position coordinate at any instant t is ` x = at^(4) - bt^(3) + 2 ct^(2) - (3d)t` where a,b,c,d are constants What is the force acting on the particle at instant ?

Answer

`F = m (12at^(2) - 6bt +2c)`

Explanation

Here, `x = at^(4) - bt^(3) + 2 ct^(2) - 3 d (t)`
velocity, `upsilon = (dx)/(dt) = 4 at^(3) - 3 bt^(2) + 2 ct - 3 d`
Acceleration, `a = (d upsilon)/(dt) = 12 at^(2) - 6 bt + 2 c`
Force `F = ma = m(12 at^(2) - 6 bt + 2 c)` .