Question

The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of a force F such that the force F is directly proportional to t is

• A. Directly proportional to t²
• B. Independent of t
• C. Directly proportional to t⁴
• D. Directly proportional to t

Answer 1

The correct option is C

Directly proportional to t⁴

f = kt

$m{\int }_0^v$ dv = $k{\int }_0^t$ tdt
mv = k$t^2$
v = $\frac{k}{m}$$t^2$
KE = $\frac{1}{2}$m$v^2$=$\frac{1}{2}$m$\frac{k^2}{m^2}$$t^4$ = $($$\frac{k^2}{2m}$ $)$$t^4$
KE $\alpha$ $t^4$