Does not accelerate while driving and brakes become stiff

While driving, the car suddenly slows and will not pick up speed much even when you step harder on the gas pedal; usually happen when have to ease on the gas pedal while driving on a gentle up slope. Tried stepping on the brake and realized it was becoming hard. Problem resolved by itself when switched off the engine and rested till the brake stiffness is gone.

No problem light appears on the dashboard at all.

If reversing before rested, the car will jerk and stall.

Replaced the PCV value and check valve to brake booster but problem not resolved.