"If the object has a speed of" -2.5 m/s at x = 0m, find its speed at x = 5.00 m and its speed at x = 15.0 m.

Hello your question has some missing parts attached below is the missing part

A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below.

answer : speed at x = 5 m = 3.35 m/s

              speed at x = 15m  = 5.12 m/s

Explanation:

initial speed( x = 0 ) = 2.5 m/s

speed at x = 5.00 m = ?

speed at x = 15 m = ?

Determine speed at x = 5 m

First we will apply the expression for work-energy theorem

w =  ----- ( 1 )

where : w = 7.50J, = 2.5m/s , m = 3.0 kg ( in the expression of work )

input values into equation 1

7.50 = 1/2 (3 ) ( v^2 - 2.5^2 )

7.50 = 3/2 ( v^2 - 6.25 )

5 j/kg = v^2 - 6.25

∴ v = √11.25 = 3.35 m/s

Determine speed at X = 15

first we will determine the work done form x = 5 to x = 15

W = 7.5J + 15J + 7.5J = 30J,   = 2.5m/s , m = 3.0 kg

w = --- ( 2 )

equation2 becomes

30J = 1/2 ( 3 ) ( v^2 - 6.25 )

30J = 3/2 ( V^2 - 6.25 )

20 J/kg = v^2 - 6.25

v = √26.25 = 5.12 m/s

the answer would be c. motion and direction

i hope this : )