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.

The relationship between acceleration and velocity is:

Acceleration is equal to the change in velocity over the change in time. If the object starts from rest, then we can set up an equation to solve for the change in velocity.

Using the terms from the question, we can see that the acceleration will be equal to the final velocity divided by the time.

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

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

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

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

The equation for distance travelled in the x-direction with parabolic motion is .

The mass of the object is not a variable in this calculation, and will not alter the horizontal velocity.

This can also be observed by analyzing the units for the velocity calculation.

Kilograms are not involved in the units, so mass will not be involved.

Changing the mass will not change the distance travelled; the rock will travel the same distance.

The equation for distance travelled in the horizontal direction is:

There is no acceleration in the horizontal direction, so this velocity is constant throughout flight.

There is no place for mass in this equation. Any objects thrown with the same velocity will travel the same distance. The two rocks with thus travel the same horizontal distance.

Knowns:

Unknowns:

Equation:

The most important thing to recognize here is that the initial and final velocities are not in the correct units.  The first step is to convert both of these values to .

Then rearrange your equation to solve for  (the missing variable).

Now plug in the variables and solve.