The initial velocity and acceleration of four moving objects at a given instant in time are given in the following table. Determine the final speed of each of the objects, assuming that the time elapsed since t = 0 s is 2.0 s.

initial velocity accerlation
+13m/s -3.3m/s^2
+13m/s -3.5m/s^2
-12m/s +3.1m/s^2
-13m/s -3.0m/s^2

1. Vf = Vi + at.

Vf = 13 + (-3.3)2,
Vf = 13 - 6.6 = 6.4m/s.

The remaining problems are the same.

6.4

Well, it seems like we have some moving objects here! Let's find out their final speeds after 2.0 seconds.

For the first object, it started with an initial velocity of +13 m/s and has an acceleration of -3.3 m/s^2. So, after 2.0 seconds, we can use the equation:

final speed = initial velocity + (acceleration × time)

final speed = 13 m/s + (-3.3 m/s^2 × 2.0 s)

final speed = 13 m/s - 6.6 m/s

final speed = 6.4 m/s

For the second object, it also had an initial velocity of +13 m/s but with an acceleration of -3.5 m/s^2:

final speed = 13 m/s + (-3.5 m/s^2 × 2.0 s)

final speed = 13 m/s - 7.0 m/s

final speed = 6.0 m/s

Moving on to the third object, it started with an initial velocity of -12 m/s and had an acceleration of +3.1 m/s^2:

final speed = -12 m/s + (3.1 m/s^2 × 2.0 s)

final speed = -12 m/s + 6.2 m/s

final speed = -5.8 m/s

Lastly, the fourth object had an initial velocity of -13 m/s and an acceleration of -3.0 m/s^2:

final speed = -13 m/s + (-3.0 m/s^2 × 2.0 s)

final speed = -13 m/s - 6.0 m/s

final speed = -19 m/s

So, after 2.0 seconds, the final speeds of the objects are:

Object 1: 6.4 m/s
Object 2: 6.0 m/s
Object 3: -5.8 m/s
Object 4: -19 m/s

Hope these results didn't give you any "speed bumps" along the way!

To determine the final speed of each object, we can use the equations of motion.

The equation for the final velocity (v) in terms of initial velocity (u), acceleration (a), and time (t) is:

v = u + at

For each object, we need to apply this equation to calculate the final velocity and then determine the final speed by taking the absolute value of the velocity because speed is a scalar quantity.

Let's calculate the final speed for each object step-by-step:

Object 1:
Initial velocity (u1) = +13 m/s
Acceleration (a1) = -3.3 m/s^2
Time (t) = 2.0 s

Using the equation v = u + at, we have:
v1 = 13 m/s + (-3.3 m/s^2) * 2.0 s
v1 = 13 m/s - 6.6 m/s
v1 = 6.4 m/s

Final speed (s1) = |v1| = |-6.4 m/s| = 6.4 m/s

Object 2:
Initial velocity (u2) = +13 m/s
Acceleration (a2) = -3.5 m/s^2
Time (t) = 2.0 s

Using the equation v = u + at, we have:
v2 = 13 m/s + (-3.5 m/s^2) * 2.0 s
v2 = 13 m/s - 7 m/s
v2 = 6 m/s

Final speed (s2) = |v2| = |6 m/s| = 6 m/s

Object 3:
Initial velocity (u3) = -12 m/s
Acceleration (a3) = +3.1 m/s^2
Time (t) = 2.0 s

Using the equation v = u + at, we have:
v3 = -12 m/s + (3.1 m/s^2) * 2.0 s
v3 = -12 m/s + 6.2 m/s
v3 = -5.8 m/s

Final speed (s3) = |v3| = |-5.8 m/s| = 5.8 m/s

Object 4:
Initial velocity (u4) = -13 m/s
Acceleration (a4) = -3.0 m/s^2
Time (t) = 2.0 s

Using the equation v = u + at, we have:
v4 = -13 m/s + (-3.0 m/s^2) * 2.0 s
v4 = -13 m/s - 6.0 m/s
v4 = -19 m/s

Final speed (s4) = |v4| = |-19 m/s| = 19 m/s

Therefore, the final speeds of the four objects are:
Object 1: 6.4 m/s
Object 2: 6 m/s
Object 3: 5.8 m/s
Object 4: 19 m/s