The smallest speed is zero which occurs during the final intervals, which have a slope of zero.

The smallest speed is zero, which occurs during the final intervals which shows no change in position.

The largest and only positive velocity occurs during the first interval when the slope is positive.

The largest positive velocity occurs during the period with the maximum positive change in position. This is the first period.

Negative velocities correspond to periods when the position decreases in value. The largest negative velocity occurs during the third period.

The position decline the largest amount per unit time during the third interval.

Displacement has magnitude and direction. It is found by subtracting the position at time zero from the position at time ten seconds.

Displacement has direction and magnitude. To determine the displacement, subtract the final position from the initial position, and keep the sign, which shows us direction. Alternatively, we can correctly say that Boomer's displacement is  south. 

To solve this problem, we'll need to use a formula that can relate distance to acceleration and time. It's also worth noting that in this case, we are only considering vertical motion along the y-axis. We don't have to worry about horizontal motion along the x-axis.

 is the vertical displacement

 is the initial velocity in the vertical direction

 is time

 is the acceleration due to gravity (which is only in the vertical direction)

Since the object is starting from rest, the initial velocity will be equal to zero, which cancels out the  term and gives us:

Rearranging to solve for , we obtain:

To answer this question, we'll first need to find the distance the car travels before coming to a stop. Since we are told in the question stem that the car is decelerating at a constant rate, we know that we have a situation in which acceleration is constant and thus we can make use of the kinematic equations.

And since we know that the car is coming to a stop, we know that our final velocity will be equal to zero.

Furthermore, since we know the car is decelerating, we know it is slowing down and is thus accelerating in the direction opposite to its direction of motion. So if we assign a positive value to the velocity, then the acceleration will have a negative value.

Now that we have found the distance traveled by the car, we can calculate the amount of time it takes for the car to come to a stop.

Plug in known values and solve.

From the above expression, we see that there are two solutions that can satisfy the value of . Only one of them, however, will make any sense physically. To solve for the two values, we will need to use the quadratic equation.

Our known values for the variables above are as follows: 

Plug into the quadratic equation and solve.

 and . The negative value makes no sense physically, thus our answer is .

An alternative (and much faster) way of solving this problem that yields the same answer is to use the following equation.

We know that our final velocity is equal to zero since the car is coming to a stop, and we're told in the question stem that we're dealing with a constant deceleration (negative acceleration).