Select all layers and precompose them!
I will call this composition 'Motorcycle Explosion'.
Reveal the position property of the layer and alt click on the stop watch icon to enable the expression editor. Into the text field, type'wiggle(20, '
and then use the pickwhip icon to select the value of the slider effect to insert it into the expression.
Finish off the expression with ');'. The final expression should say something like 'wiggle(20, effect("Slider Control")("Slider"));'.
The value of the slider now controls the amount of random offset that will be applied to the position of the explosion layer. Animate the slider to increase from 0 to around 100 when the explosion hits and then slowly decrease back to 0.
This will cause the layer to shake when the explosion hits. You will see the background of the composition when the layer moves around but you can fix this simply by scaling the layer up as needed. Alternatively you could use the Motion Tile effect to mirror the edges of the layer as it moves around during the shake effect.
Finally, enable motion blur on the layer to add some realism to the shake effect.