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
(a) +12 m/s
(b) +12 m/s
(c) -13 m/s
(d) -13 m/s
Acceleration
(a) +3.0 m/s
(b) -2.8 m/s
(c) +3.4 m/s
(d) -2.6 m/s
v = vo + at. Plug. Chug.
To determine the final speed of each object, we need to use the equations of motion. The equation we will use is:
v = u + at
where:
- v is the final velocity (speed)
- u is the initial velocity
- a is the acceleration
- t is the time elapsed
Let's calculate the final speed for each object.
For object (a):
Initial velocity (u) = +12 m/s
Acceleration (a) = +3.0 m/s
Time elapsed (t) = 2.0 s
Using the equation v = u + at:
v = 12 m/s + (3.0 m/s)(2.0 s)
v = 12 m/s + 6 m/s
v = 18 m/s
So, the final speed of object (a) is 18 m/s.
For object (b):
Initial velocity (u) = +12 m/s
Acceleration (a) = -2.8 m/s
Time elapsed (t) = 2.0 s
Using the equation v = u + at:
v = 12 m/s + (-2.8 m/s)(2.0 s)
v = 12 m/s + (-5.6 m/s)
v = 6.4 m/s
So, the final speed of object (b) is 6.4 m/s.
For object (c):
Initial velocity (u) = -13 m/s
Acceleration (a) = +3.4 m/s
Time elapsed (t) = 2.0 s
Using the equation v = u + at:
v = -13 m/s + (3.4 m/s)(2.0 s)
v = -13 m/s + 6.8 m/s
v = -6.2 m/s
So, the final speed of object (c) is 6.2 m/s.
For object (d):
Initial velocity (u) = -13 m/s
Acceleration (a) = -2.6 m/s
Time elapsed (t) = 2.0 s
Using the equation v = u + at:
v = -13 m/s + (-2.6 m/s)(2.0 s)
v = -13 m/s + (-5.2 m/s)
v = -18.2 m/s
So, the final speed of object (d) is 18.2 m/s.
Therefore, the final speeds of the four objects are as follows:
(a) 18 m/s
(b) 6.4 m/s
(c) -6.2 m/s
(d) -18.2 m/s