If the observer sees the bicycle moving with a uniform velocity , then that means all the parts of the bicycle together are moving with the same velocity. The dog, the cyclist, the handlebars, everything in the system (that is not moving independently, such as the pedals or the wheels) is moving with the same velocity .

To solve this problem we need to consider the definition of speed, which is the distance traveled over a given amount of time.

Even though the player's speed is changing throughout the sprint (due to acceleration), we are asked to find the average speed. We can do this using the total distance and total time given. The distance is and the time is .

To solve this problem, we use the relation between velocity and time:

We can rearrange this equation to isolate the variable for time:

Use the given distance and velocity to solve for the time.

Velocity is a vector measurement of displacement per unit time. This means that it has both magnitude and direction, according to the direction of the displacement.

The standard unit for displacement is meters and the standard unit for time is seconds; thus, the SI unit for velocity is meters per second. Any standard measure of velocity will be given in meters per second, with a corresponding direction of action.

Velocity is equal to a change in displacement per unit time. Consider a basic velocity vs. time graph that depicts a constant velocity, given by a straight horizontal line. How can we determine the displacement during a given time interval? Use the kinematics equation:

Acceleration will be zero, allowing us to reduce the equation. We can also assume that there is zero initial displacement.

So, the displacement will be equal to the velocity multiplied by the time. In the graph, velocity will be represented by the vertical location and time will be represented by the horizontal location of any point. Displacement will be equal to the height of the graph times the width of the graph, or the area of the rectangle created by the constant velocity over a unit of time.

Though this is just one example, displacement will always be equal to the area under the curve of a velocity vs. time graph.

In calculus terms, velocity is the derivative of the function for displacement in terms of time. To find the displacement, one must take the integral of the velocity function. The result is the area under the curve of the velocity function.

The important thing to note is that the question asks for the velocity at any given point. The average velocity will be equal to the total displacement divided by the total time, but the question is asking for the instantaneous velocity.

Velocity is calculated by a change in displacement over a change in time. In a displacement versus time graph, this is equal to the slope.

This tells us that the slope at a certain time will be equal to the velocity at that time.

In calculus terms, velocity is the derivative of the function for displacement in terms of time. What this means is that at any point on the graph, the instantaneous slope is the velocity for that given time. To determine velocity, one must find the slope of the line at that particular time interval.

The relationship between velocity, distance, and time is:

We can multiply both sides by  to see solve for the distance traveled, in terms of the time and velocity.

The product of time and velocity, , will give us the distance we are looking for.

Since the ball starts with a positive velocity and ends at rest, we can predict that the acceleration will be negative. Using the values given in the question and the equation below, we can solve for the acceleration.

Notice that at the beginning and at the end of the problem, the velocity of the object is . Acceleration is . Since there is no change in velocity, acceleration is calculated as , so the acceleration is .

Acceleration is a vector. This means that positive and negative signs are used to help us understand the direction of motion. If something has a negative acceleration it CAN mean that it is slowing down, but not always. Negative usually means that an object is moving to the left, down, or backwards. If the ball begins from rest, and has a negative acceleration, then it is gaining a negative velocity. This simply refers to a velocity in a negative, or backwards, direction.