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.

Knowns:

Unknowns: 

Equation:

Since both trains are traveling at a constant velocity and there is no acceleration the equation is

Rearrange this equation to solve for time.

Since both trains are traveling at the same speed, the trains will meet up in the middle of the total distance between the trains.

Plug this distance into the equation to find the time that it takes to travel the distance.

The answers provided are in minutes, so the final step is to convert the time to minutes.

Knowns:

Unknowns:

Equation:

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.

Knowns:

Unknowns:

Equation:

The easiest way to approach this problem is find the average velocity, multiply by 2 because the car started from rest, and then divide the final velocity by time to get the acceleration. 

Average velocity:

The final velocity is  because the car started from rest. This is evident from the equation for average velocity if we solve for final velocity:

To find the acceleration use the acceleration equation with the final velocity that was just calculated.

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 have a negative velocity the object must be traveling in the  direction.  The direction on the velocity vector indicates the direction of the motion of the object

If the velocity vector and acceleration vectors are pointing in opposite directions, then the object must be slowing down as the acceleration vector is opposing the motion of the object.

Therefore the object is traveling in the  direction and decreasing in speed.