Asingle conservative force vector f = (4.0x - 12)i hat n where x is in meters, acts on a particle moving along an x axis. the potential energy u associated with this force is assigned a value of 20 j at x = 0. (a) write an expression for u as a function of x, with u in joules and x in meters.

(4.0x - 12)i . (5/3)i

Step-by-step explanation:

Potential energy = Workdone

Workdone = Force x distance

Force = F = (4.0x - 12)i  N

Workdone = 20J

At  x= 0

F = -12i

/F/= 12

Workdone = Force  x distance

20  =   12 x   distance

Distance =  20/12

               =  5/3

In the vector form  distance is written as (5/3)i

Since Workdone/ Energy is scalar, U can be expressed as a dot product of  the vectors of Force and distance :

(4.0 x - 12)i . (5/3)i

7200

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