A truck covers 40.0 m in 7.00 s while smoothly slowing down to a final velocity of 2.45 m/s.

What is the question? Do you want to know the initial velocity? The deceleration rate?

Since the average velocity is 40/7 = 5.714 m/s, the initial velocity Vo is given by
(Vo + 2.45)/2 = 5.714
Vo = 8.98 m/s

The deceleration rate, a, can be calculated using

a = (Vo - 2.45)/7.00 = ___

original speed and acceleration

That is what I have derived for you

To find the acceleration of the truck, you can use the formula:

acceleration = (final velocity - initial velocity) / time

In this case, the initial velocity is not given, but since the truck is "smoothly slowing down," we can assume that the initial velocity is greater than the final velocity (2.45 m/s in this case).

Let's assume the initial velocity of the truck is "vi."

Using the given values, we have:
final velocity (vf) = 2.45 m/s
time (t) = 7.00 s

So the equation becomes:
acceleration = (2.45 m/s - vi) / 7.00 s

To find the initial velocity (vi), we need to determine the distance covered by the truck while decelerating. We can do this by using the formula:

distance = (initial velocity + final velocity) / 2 * time

Here, the final velocity is 2.45 m/s, and the time is 7.00 s. The distance covered is given as 40.0 m.

Plugging in the values, we have:
40.0 m = (vi + 2.45 m/s) / 2 * 7.00 s

Now we can solve this equation to find the initial velocity (vi).

Rearranging the formula, we get:
vi + 2.45 m/s = (40.0 m * 2) / 7.00 s
vi + 2.45 m/s = 11.43 m/s

Subtracting 2.45 m/s from both sides, we get:
vi = 11.43 m/s - 2.45 m/s
vi = 8.98 m/s

Now that we have found the initial velocity (vi), we can substitute it back into the acceleration formula:

acceleration = (2.45 m/s - 8.98 m/s) / 7.00 s

Simplifying this equation, we get:
acceleration = -6.53 m/s / 7.00 s
acceleration = -0.932857 m/s²

So, the acceleration of the truck is approximately -0.932857 m/s² (negative because the truck is slowing down).