In an experiment, a variable, position-dependent force F(x) is exerted on a block of mass 1.0kg that is moving on a horizontal surface. The frictional force between the block and the surface has a constant magnitude of Ff . In addition to the final velocity of the block, which of the following information would students need to test the hypothesis that the work done by the net force on the block is equal to the change in kinetic energy of the block as the block moves from x=0 to x=5m ?
(A) The function F(x) for 0 < x < 5 and the value of Ff.
(B) The function a(t) for the time interval of travel and the value of Ff.
(C) The function F(x) for 0 < x < 5, the block's initial velocity, and the value of Ff.
(D) The function a(t) for the time interval of travel, the time it takes the block to move 5 m, and the value of Ff.
(E) The block's initial velocity, the time it takes the block to move 5 m, and the value of Ff.

correct option is C

The function F(x) for 0 < x < 5, the block's initial velocity, and the value of Ff. 

Step-by-step explanation:

The total work done = P.E + K.E

K.E = 1/2mv^2

The speed V depends on the position:

0 < x < 5

Also, since work done = F × distance x

The workdone also depends on F(x)

The net force = 0 that is

F + fr = 0

Where fr = frictional force.

Therefore the best option for the hypothesis of work done will be;

The function F(x) for 0 < x < 5, the block's initial velocity, and the value of Ff. 

if x = 1, then the answer is 3.5

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph