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 2.2 s.
To determine the final speed of each object, we can utilize the kinematic equation:
v = u + at
Where:
v = final velocity/speed
u = initial velocity
a = acceleration
t = time elapsed
Given the initial velocity (u) and acceleration (a) for each object, we can substitute these values into the equation along with the time elapsed (t = 2.2 s) to find the final speed (v) for each object.
Let's calculate the final speed (v) for each of the four objects:
Object 1:
Initial velocity (u) = 8 m/s
Acceleration (a) = 4 m/s^2
Time elapsed (t) = 2.2 s
v = u + at
v = 8 + 4 * 2.2
v = 8 + 8.8
v = 16.8 m/s
Therefore, the final speed of Object 1 is 16.8 m/s.
Object 2:
Initial velocity (u) = -5 m/s
Acceleration (a) = -2.5 m/s^2
Time elapsed (t) = 2.2 s
v = u + at
v = -5 + (-2.5) * 2.2
v = -5 + (-5.5)
v = -10.5 m/s
Therefore, the final speed of Object 2 is -10.5 m/s.
Object 3:
Initial velocity (u) = 0 m/s
Acceleration (a) = -9.81 m/s^2 (assuming gravitational acceleration)
Time elapsed (t) = 2.2 s
v = u + at
v = 0 + (-9.81) * 2.2
v = 0 - 21.582
v = -21.582 m/s
Therefore, the final speed of Object 3 is -21.582 m/s.
Object 4:
Initial velocity (u) = 12 m/s
Acceleration (a) = 0 m/s^2 (assuming no acceleration)
Time elapsed (t) = 2.2 s
v = u + at
v = 12 + 0 * 2.2
v = 12 + 0
v = 12 m/s
Therefore, the final speed of Object 4 is 12 m/s.
In summary:
Object 1: Final speed = 16.8 m/s
Object 2: Final speed = -10.5 m/s
Object 3: Final speed = -21.582 m/s
Object 4: Final speed = 12 m/s
To determine the final speed of each object, we need to use the equations of motion. The equations we'll be using are:
1. Final velocity (v) = Initial velocity (u) + (acceleration (a) x time (t))
2. Final speed (v) = |Final velocity (v)|
Let's use the given data and equations to find the final speed for each object:
Object | Initial Velocity (m/s) | Acceleration (m/s^2)
----------------------------------------------------------
Object 1 | 5.0 | 2.0
Object 2 | 10.0 | 0.0
Object 3 | 0.0 | -9.8
Object 4 | -2.0 | 4.2
For Object 1:
Using equation 1: v = 5.0 + (2.0 x 2.2)
v = 5.0 + 4.4
v = 9.4 m/s
Using equation 2: v = |9.4|
v = 9.4 m/s
So, the final speed of Object 1 is 9.4 m/s.
For Object 2:
Using equation 1: v = 10.0 + (0.0 x 2.2)
v = 10.0 + 0.0
v = 10.0 m/s
Using equation 2: v = |10.0|
v = 10.0 m/s
So, the final speed of Object 2 is 10.0 m/s.
For Object 3:
Using equation 1: v = 0.0 + (-9.8 x 2.2)
v = 0.0 - 21.56
v = -21.56 m/s
Using equation 2: v = |-21.56|
v = 21.56 m/s
So, the final speed of Object 3 is 21.56 m/s.
For Object 4:
Using equation 1: v = -2.0 + (4.2 x 2.2)
v = -2.0 + 9.24
v = 7.24 m/s
Using equation 2: v = |7.24|
v = 7.24 m/s
So, the final speed of Object 4 is 7.24 m/s.
Therefore, the final speed of the four objects, after 2.2 seconds, are as follows:
Object 1: 9.4 m/s
Object 2: 10.0 m/s
Object 3: 21.56 m/s
Object 4: 7.24 m/s