In lesson 1 we examined Newton's first law: objects move with constant (possibly zero) velocity unless something exerts a force on them to change their velocity. We don't yet know much about how that change in velocity works. We'll see that in this lesson.
In the first activity you were asked to find the acceleration of three carts using the kinematic relationship d=1/2at^2. You looked at three videos. We can use the first video to establish a reference for comparison. We applied a force to a cart and measured its acceleration. We then changed the force that we applied to the cart, and then changed the mass of the cart. What you hopefully saw was that doubling the mass of the cart roughly halved the acceleration it felt. At the same time applying twice the force to the cart caused it to experience roughly twice the acceleration. Scientifically this is not enough observation to establish a relationship between force, mass and acceleration, but others in the past have done much more observation and we can compare our results with theirs. Their observations are that the net force, F, is related to the mass of an object, m, and its acceleration, a, by the equation F=ma. In this experiment we indeed saw that keeping F fixed, and doubling m resulted in a being halved. Similarly keeping m fixed and doubling F results in a being doubled as well. So although we haven't proven F=ma our observations definitely imply it. This is what Newton's second law says: the net force felt by an object is equal to its mass multiplied by its acceleration. Remember that acceleration is the rate at which an object's velocity is changing in time, so Newton's second law tells us how forces change an object's velocity.
In the second activity you were asked to look at two pucks experiencing two different kinds of motion. In the first video the puck was accelerated by a constant force that was provided by tilting the frictionless air-table it was sitting on. In the second video the puck was accelerated by an instantaneous force that was provided by a launching device. In this activity the key question is whether each puck feel a force. The answer is yes, but with strong qualifiers. The first puck feels a constant force that acts over the course of its entire motion. As a result we see that over constant time intervals it moves a greater and greater distance. This indicates that its velocity is changing; it is accelerating. The second puck, however feels a force only while it is in contact with the launcher. During that time it accelerates because its initial velocity is zero, and its final velocity is not, but once it leaves the launcher it moves the same displacement in every time interval, so its velocity is constant. This shows us that an object's velocity only changes, that is the object accelerates, while the force is actually acting on it. This is important to note.
In the third activity we looked at the effect of a force on direction of motion. In this exercise we can see that both pucks feel a force in the vertical direction, due to gravity, but the red puck also feels an impulsive force due to the launcher. This shows us two important things. The first is that forces in one direction don't affect the motion of an object in a direction perpendicular to the force. The second is that a force can change the direction of an object's motion. Remember force causes acceleration, which is a change in an object's velocity. However, don't forget that velocity is a vector so it has both a magnitude and a direction. If either (or both) changes the object is accelerating.