Backward jerk in Earth's frame? When the bus starts suddenly it accelerates and we experience a backward jolt, now since the Earth is continuously accelerating through space time why don't we experience that jolt here on earth itself?
 A: Acceleration can be defined as a rate of change in velocity per unit time.  Velocity is a vector, which consists of both direction and magnitude.  Change of either will result in acceleration.
Because the Earth rotates on its axis and follows a curved trajectory around the Sun, it continually undergoes a change of direction type of acceleration. The magnitude of the Earth's velocity vector (speed) remains roughly constant, but the direction of the velocity vector changes constantly.
Our natural tendency is to fly off in a straight line into space as the surface of the Earth rotates away from under us.  This tendency (measured from the Earth's rotating inertial frame of reference) is called centrifugal force.  But we don't feel any acceleration from that centrifugal force, as it's the Earth that accelerates away from us, rather than we accelerating away from the Earth.  What we do feel is the centripetal force that keeps our inertia from carrying us away from the Earth, as the Earth accelerates away from us.
Gravity keeps us tethered to the surface of the Earth.  Gravity provides the centripetal force that keeps us from flying into space as the Earth accelerates away from us.  Our weight is the feeling we have from the centripetal force of the Earth's gravity which keeps us from continuing in a straight line away from the rotating Earth.
If the Earth's acceleration suddenly were to change, we would feel a jolt.  If the rate of spin changed appreciably, for example, even gravity might not be able to keep us from sliding backwards or forwards, or even off the planet entirely.  We have grown used to the steady directional acceleration of the Earth, and to the centripetal force that tethers us to the Earth's surface, so we don't notice it.
A: Well, it's just that the centripetal acceleration is not that big. If you take the acceleration to be
$$
a_{centrip} = r\omega^2
$$
and plug in various numbers, you get that the centripetal acceleration from Earth's rotation around itself is 0.3% of the gravitational acceleration and the acceleration from Earth's rotation around the sun is 0.06% of the gravitational acceleration.
A: There are two causes of acceleration: 1) change in speed, and 2) change in direction. Only the first type results in the jerk you describe. The accelerations we experience on Earth"s surface are the second type.  We feel them as small decrement in our weight compared to what we would weigh if the Earth were neither spinning nor rotating in its orbit about the sun. Since this decrement is relatively constant, we feel no jerk
A: The jolt or jerk (a technical term!) which you experience is caused by a sudden change in acceleration. When the bus starts moving it changes from zero acceleration to some positive acceleration. Even if the speed has not changed much, there is a sudden increase in acceleration. The same happens when you brake and the vehicle stops with a jolt.
The Earth is accelerating constantly round the Sun, and we are accelerating constantly as it rotates. In neither of these cases is there any sudden change in acceleration. There is no jerk.
See also :
Why does one experience a short pull in the wrong direction when a vehicle stops?
Bidirectional jerk motion on a stopping vehicle
How to brake 'beautifully'?
