The force applied against an object moving horizontally on a linear path is described by $F (x) = cos π x + 1$ $F(x)= cospix+1$ . By how much does the object's kinetic energy change as the object moves from $x \in [0, 3]$ $x in [ 0, 3 ]$ ?

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The force applied against an object moving horizontally on a linear path is described by $F (x) = cos π x + 1$ $F(x)= cospix+1$ . By how much does the object's kinetic energy change as the object moves from $x \in [0, 3]$ $x in [ 0, 3 ]$ ?

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Answer 1 · 2018-03-31T23:13:18

The change in kinetic energy will be $3$ $3$ joules.

Explanation:

Recall that $"Work" = F * d = Delta KE$

Therefore, if we find $F * d$ one $[0, 3]$ , we'll have our change in kinetic energy. Therefore, we will have to integrate the force function on $[0, 3]$ .

$I = int_0^3 cos(pix) + 1$

$I = [1/pi sin(pix) + x]_0^3$

$I = 1/pisin(3pi) + 3 - 1/pisin(0) - 0$

$I = 3$

Therefore the change in kinetic energy will be $3$ Joules.

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The force applied against an object moving horizontally on a linear path is described by $F (x) = cos π x + 1$ $F(x)= cospix+1$ . By how much does the object's kinetic energy change as the object moves from $x \in [0, 3]$ $x in [ 0, 3 ]$ ?

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Explanation:

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The force applied against an object moving horizontally on a linear path is described by F(x)= cospix+1 F(x)=cosπx+1F(x)= cospix+1 . By how much does the object's kinetic energy change as the object moves from x in [ 0, 3 ]x∈[0,3] x in [ 0, 3 ]?

1 Answer

Explanation:

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The force applied against an object moving horizontally on a linear path is described by $F (x) = cos π x + 1$ $F(x)= cospix+1$ . By how much does the object's kinetic energy change as the object moves from $x \in [0, 3]$ $x in [ 0, 3 ]$ ?