Question

Fifteen joules of work is done on object A (at rest), all of which goes into changing its kinetic energy. Sixty joules of work is done on object on object B (at rest and with same mass as object A), all of which goes into changing its kinetic energy.
How does the speed of object B compare to the speed of object A after this work is done ?

• A. The speed of object B is four times as much as the speed of object A.
• B. The speed of object B is sixteen times as much as the speed of object A.
• C. The speed of object B is two times as much as the speed of object A.
• D. The speed of object B is less than two times as much as the speed of object A (but not the same as ).
• E. The speed of object B is the same as the speed of object A.

Answer 1

The correct option is C The speed of object B is two times as much as the speed of object A.

$ForobjectAW=\frac{1}{2}m{v_A}^2=15ForobjectBW=\frac{1}{2}m{v_B}^2=60\Rightarrow \frac{{v_A}^2}{{v_B}^2}=\frac{15}{60}\Rightarrow \frac{d{v}_A}{v_B}=\sqrt{\frac{1}{4}}=\frac{1}{2}\Rightarrow v_B={2v}_A$