# I have a question about explanation of inertia of motion of a body by pseudo force

If a bus stops moving suddenly, we tend to fall forwards due to the inertia of motion of our upper body. But can we explain the sudden jerk in the forward direction due to some pseudo force? (Because I think according to an observer on the ground [inertial frame], the bus is a non-inertial frame {it is accelerating} - therefore pseudo force can be applied).

But can we show this sudden jerk in the forward direction due to pseudo force? Like this image showing this phenomenon in the train? [How can pseudo force be applied here instead of the inertia of motion].

• From the perspective of an observer in the bus, the pseudo force is zero while the bus is moving at constant velocity, then, as it starts breaking, the pseudo force appears out of nowhere (has no obvious source), and grows quickly to some value, lasts a short while, then drops back to zero when the bus stops. The forward acceleration of any object is then attributed to this pseudo force. Jul 5, 2022 at 16:24
• Can you write as an equation using the mass and acceleration? Jul 5, 2022 at 16:35
• In a non-inertial reference frame, the apparent force is the sum of all the forces, including the pseudo force $F_p$. So, in this case, the pseudo force, the force of gravity, the normal force and the tension from the bus-straps: $F = F_p + F_g + N + T = ma$ (assuming the person is a rigid body). If this was a person floating in an accelerating spaceship, the pseudo force would just be $ma$, for the person's acceleration measured from the POV of the spaceship itself. In a bus, it gets more complicated because $F_p + F_g$ combine to pull you at an angle, and $T$ varies with time. Jul 5, 2022 at 17:38