9702_s22_qp_12 Question 18

 A student attempts to derive the formula for kinetic energy E_K. She begins by considering an object of mass m which is initially at rest. A constant force F applied to the object causes it to accelerate to final velocity v in displacement s. The kinetic energy gained by the object is equal to the work done on the object by the force F.

Which equation would the student not need in order to derive the formula for E_K?

A F = ma 

B W = Fs 

C E = 1/2 Fs

D v² = u² + 2as

ANSWER: C

The Physics Behind

• E_K is derived by the above mentioned student, likely, as follows.
• E_K = W
• E_K = Fs since W = Fd
• E_K = mas since F = ma
• E_K = m(1/2 (v² -u²)  since v² = u² + 2as
• The resulting equation can therefore be simplified by considering that u = 0 as the object was initially at rest.

E_K = 1/2 mv².

• You should notice that all equations in the options except that in option C are used.