Gina is driving her car down the street. she has a teddy bear sitting on the back seat. a dog runs in front of gina's car, so she quickly applies the brakes. the force of the brakes causes the car to stop, but the teddy bear continues to move forward until it hits the car's dashboard. why the teddy bear did not stop moving until it hit the car’s dashboard?

This is due to the law of inertia, an object at rest stays at rest and an object in motion stays in motion unless acted upon an unbalanced force.

So when you are traveling in a car I'm assuming the driver Gina is wearing her seatbelt, when Gina hits her brakes that is the "unbalanced force".  By hitting the brakes Gina will also nudge forward but is stopped by her seatbelt from going too far forward.  The teddy bear is not so lucky and since he's not wearing a seatbelt he is propelled forward hitting the dashboard.  Poor Teddy.

0.19 m/s and 0.45 m/s

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.