A vector quantity has has both magnitude and direction. By definition, only velocity satisfies these criteria.

Distance, angle, and speed have magnitude, but no direction.

The answer to this question lies within Newton's third law: for every action, there is an equal and opposite reaction. If the large ball applies a  force on the smaller ball, the smaller ball will apply a  force on the large ball in the opposite (negative) direction.

This is a conservation of energy question. The event is the collision. The initial energy can be calculated by gravitational potential energy:

The final total energy must be the same. The energy of the scattered pieces must add to 

When the rope is around the pulley, the acceleration is slower due to internal friction, thus the initial acceleration of the platform would be lower. Once the platform was in free fall, however, the acceleration due to gravity is constant at 9.8 m/s²; thus, the final acceleration of the platform is the same in both scenarios.

This is a question that helps you see how displacement and velocity compare to distance and speed, respectively. Remember that the runner starts and stops at the same point on the track, so her total displacement is zero feet.

Since , the runner's average velocity is . Since the runner's average speed is greater than her average velocity, we can conclude this is the correct answer. Her average speed refers to her distance, rather than displacement, and is greater than zero.

This is also important to remember! Since the runner changed direction on the track, she accelerated and decelerated accordingly based on her position on the track. She did not have a constant acceleration.

The three blocks must remain in contact as they move, so they will each have the same velocity and acceleration regardless of their different masses. So, .

Choice 3 is correct. Recall that physics problems tell you where to begin and end. The only thing that matters in figuring displacement is the beginning point and end point. The man effectively walked along the hypotenuse of a right triangle whose sides measured 2 km each.  Since a² + b² = c², then 4 + 4 = c², and the correct response is the square root of 8 with the direction of the displacement added for clarity.

Choice 4 is correct. In physics, it is often helpful to draw a diagram of the problem.  In this case, the respondent would draw a vector 10 hours x 10 knots from south to north (usually going towards the top of a sheet of paper) and a perpendicular vector 50 nautical miles long projecting from the arrowhead of the first vector to the left, or west. The hypotenuse of the right triangle so created is the actual path of a boat experiencing these forces. Without resorting to calculating the square root of the sum of (10,000 plus 2,500 nautical miles²), it is obvious that choice 4 is the only reasonable one.

To find total displacement, find the vector sum of the northern and eastern travel using the Pythagorean theorem.

Note that displacement differs from total distance traveled (which would be 650km).  

Since it takes the body twice the time to cover the same distance, the magnitude of v₂ is half of v₁. Also note that the direction of the body has reversed (velocity is a vector quantity), and so v₂ must be negative, with regard to v₁.

v = d/t

v₁ = d/2

v₂ = -d/4

v₂ = (-1/2)v₁