Why does force cause acceleration? Consider a ball placed on a smooth plane. If you take a plank made out of wood and whack it (apply a force on it), does it accelerate because 


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*First, the force compresses the part of the ball in contact and hence the ball is now like a compressed spring with potential energy
2.Next, the ball pushes on the plank using the potential energy and pushes off in the direction of force.
Is this how a force on a body at rest causes motion? If so do perfectly rigid bodies accelerate on the application of force?
 A: I am not sure that i understand your question 100%
If your question is - as mentioned in the title 'why does force cause acceleration '- then the answer is
simple: the Newton's second law of motion  (the net force on an object is equal to the rate of change 
 of its linear momentum p in an inertial reference frame) which is an axiom.
But then you continue with a description of how a force is transmited when two object collide each other.
If this is your question then the answer is : the electrostatic repulsion as very nicely is explained here:
https://www.quora.com/What-does-it-mean-for-two-things-to-be-touching
In general, each type of force is considered to have a particle 'carrier'. You can find informations
about 'force carrier' here : https://en.wikipedia.org/wiki/Force_carrier
A: Force is mass times acceleration, so the force you're applying is the torque force caused by rotating that wooden plank with a certain mass with a certain acceleration.  When you hit the ball, at an atomic level, the atoms colliding with the plank violently push its neighbors.  Its neighbors, not having any leeway, push its neighbors just as violently and so forth until the atoms in the entire ball have roughly the same force being applied.  This action is applied quickly and almost instantaneously.  
I say roughly, because internally, the movement of force being applied to the ball is a bit like a wave that travels through the ball.  Very solid objects don't allow the wave to destabilize the object, so you achieve an average force being applied to all atoms.  Something like a soft ball with air inside would have a very springy reaction caused by the strike.  The initial wave would significantly deform the ball, and the ball would have many successive waves from rebounding from the initial deformity.  You wouldn't think so, but even golf balls deform greatly at the initial impact.  
If the object deforms enough, then a larger surface area conforms to the wooden plank and acts like a spring when it returns to its original form.  The ultimate effect is that the impact is more elastic and more energy is transferred to pushing the object forward rather than the wave simply getting absorbed as it would in more solid objects, which is why most balls used in sports equipment are designed to offer maximum elasticity according to the force being applied on average.  
Obviously something that deforms too much will explode, like an apple or a water balloon.  The same force is applied, but with more surface area, the pieces don't go as far as if the object had held together due to wind resistence.  
So in short, the force is applied to soft bodies as well as solid bodies alike when hit, however soft bodies have internal forces that deform it  which could hinder the transfer of energy as easily as it helps the transfer of energy when hit.  
I hope that answers your question.
