A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as $\frac{dK}{dt}=\gammat$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true? [JEE Adv 2018 P2]

The force applied on the particle is constant

The speed of the particle is proportional to time

The distance of the particle from the origin increases linearly with time