The explanation ofs why we get thrown back with a jerk when the stationary bus we are sitting in starts moving forward is given by :

The phenomenon of being thrown back when a stationary bus starts moving is explained by Newton's first law of motion, also known as the law of inertia [t4][t5]. This law states that an object at rest will remain at rest unless acted upon by an external force [t1][t3]. When the bus accelerates forward, the lower part of the passenger's body, which is in contact with the bus, moves forward with it [t6]. However, due to inertia, the upper part of the body tends to maintain its state of rest, resulting in a backward jerk relative to the bus's motion [t6]. This resistance to change in the state of motion is a fundamental property of mass [t4]. While Newton's second law relates force to acceleration and the third law describes action-reaction pairs, the specific tendency to remain stationary is a direct application of the first law [t3][t8].

Sources

1. [1] https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/newtons-laws-of-motion/