Does the force of friction helps us to accelerate while running? The question is to find the correct statement:
Cause of increase in kinetic energy while running is due to the work done by friction force without which he cannot run.
OR
Cause of increase in kinetic energy while running is due to the work done by internal forces of the body
Book says 2nd statement is the correct one.
Why is statement 1 not correct and what are internal force?
 A: Your body is accelerated by the muscles of the leg extending. That push of the leg muscle is considered an "internal" force, because it's parts of you pushing on other parts of you.
All the kinetic energy your body gains comes from that muscle extension:  It's a force exerted over a distance, which does work on you. In turn, that increases your speed and kinetic energy.
Friction is what keeps your foot from moving relative to the ground, so that all the extension acts to push your body. But that friction, by itself, does no work and adds no energy.
A: If friction was doing work, running would be a lot more difficult.
For work, there needs to be force and displacement, and if there's displacement of the applied friction force, that means your feet are slipping on the surface.  This slipping obviously takes away from your ability to gain forward motion.
When you are moving efficiently, there is only static friction between your feet and the ground.  This is just a stationary force, and therefore no work can be done by it.  The static friction allows you to convert that internal energy into kinetic energy.  If the friction did work, it would actually be working against the increase in kinetic energy, via slipping.
A: Static friction just holds the foot stationary. That is all.
When you take a step on the ground, the muscles in your leg press your foot backwards and the rest of your body forwards. Since the foot can't go backwards due to static friction, the rest of your body goes much more forwards, because the leg still must stretch as the muscles force it to.
So, basically, static friction makes it possible for you to push yourself away from the ground. But it isn't the force that actually does it. Just like you can push yourself away from a wall. That makes you speed up, not because the wall supplies any energy to you, but because the energy you put into jolting your arms backwards into the wall results in the rest of your body moving the opposite way since the arms ain't moving backwards.
This is Newton's 3rd law.
A: 
Cause of increase in kinetic energy while running is due to the work
  done by friction force without which he cannot run. OR Cause of
  increase in kinetic energy while running is due to the work done by
  internal forces of the body

It is the static friction force between the runners feet and the ground that propels the runner forward. See the figure of a runner below showing the forces acting upon him and by him. It is the following static friction force shown in the figure that propels the runner foward.
$$F_{f}=F_{push}Cosθ$$
In order for the runner not to slip the friction force cannot exceed the maximum static friction force also shown in the figure.
hope this helps.

A: He wouldn't move anywhere without friction but the kinetic energy would still exist if he were flailing his legs around on wet ice.
A: The book statement is correct. Having said that, the first statement is important, because without gravity pulling the runner toward the centre of the Earth, and the friction with the running track surface which this causes, there would be almost no increase in the runner's kinetic energy. He would be like someone in very slippery shoes trying to run on the polished surface of a freshly frozen ice rink, just floundering about and getting nowhere. So it is true to say that friction of running shoes against the ground helps runners to accelerate, but the increase in the runner's kinetic energy is due to the work done by his muscles.
