A mouse travels along a straight line; its distance from the origin at any time is given by the equation.
x= (8.1 cm * s^-1)t-(2.7cm * s^-2)t^2
A) Find the average velocity of the mouse in the interval from = 0 to = 1.0 .
value=?; unit= ?
B)Find the average velocity of the mouse in the interval from =0 to = 4.0 .
value?; unit= ?
Express your answer to two significant figures and include the appropriate units.
i for got to add the "t"
A)t=0 to t=10
B)t= 0 to t= 4.0
A) To find the average velocity of the mouse in the interval from 0 to 1.0, we need to find the change in distance and change in time in that interval.
First, let's find the distance at the initial time (t = 0):
x = (8.1 cm/s)(0) - (2.7 cm/s^2)(0)^2 = 0
Next, let's find the distance at t = 1.0:
x = (8.1 cm/s)(1.0 s) - (2.7 cm/s^2)(1.0 s)^2 = 5.4 cm
The change in distance is 5.4 cm - 0 cm = 5.4 cm.
The change in time is 1.0 s - 0 s = 1.0 s.
Average velocity = change in distance / change in time
Average velocity = 5.4 cm / 1.0 s = 5.4 cm/s
So, the average velocity of the mouse in the interval from 0 to 1.0 is 5.4 cm/s.
B) Similarly, for the interval from 0 to 4.0, let's find the distance at the initial time (t = 0):
x = (8.1 cm/s)(0) - (2.7 cm/s^2)(0)^2 = 0
Next, let's find the distance at t = 4.0:
x = (8.1 cm/s)(4.0 s) - (2.7 cm/s^2)(4.0 s)^2 = 86.4 cm
The change in distance is 86.4 cm - 0 cm = 86.4 cm.
The change in time is 4.0 s - 0 s = 4.0 s.
Average velocity = change in distance / change in time
Average velocity = 86.4 cm / 4.0 s = 21.6 cm/s
So, the average velocity of the mouse in the interval from 0 to 4.0 is 21.6 cm/s.
To find the average velocity of the mouse in each interval, we need to calculate the displacement of the mouse in that interval and divide it by the time interval.
A) To find the average velocity in the interval from t=0 to t=1.0, we need to subtract the initial position (t=0) from the final position (t=1.0) and divide it by the time interval (1.0 - 0 = 1.0 second).
To find the position at t=0, substitute t=0 into the equation:
x = (8.1 cm/s)(0) - (2.7 cm/s^2)(0)^2 = 0
To find the position at t=1.0, substitute t=1.0 into the equation:
x = (8.1 cm/s)(1.0 s) - (2.7 cm/s^2)(1.0 s)^2 = 5.4 cm - 2.7 cm = 2.7 cm
Therefore, the displacement of the mouse in the interval from t=0 to t=1.0 is:
Displacement = Final position - Initial position = 2.7 cm - 0 cm = 2.7 cm
Average velocity = Displacement / Time interval = 2.7 cm / 1.0 s = 2.7 cm/s
So the average velocity of the mouse in the interval from t=0 to t=1.0 is 2.7 cm/s.
B) To find the average velocity in the interval from t=0 to t=4.0, we follow the same steps as before.
To find the position at t=0, substitute t=0 into the equation:
x = (8.1 cm/s)(0) - (2.7 cm/s^2)(0)^2 = 0
To find the position at t=4.0, substitute t=4.0 into the equation:
x = (8.1 cm/s)(4.0 s) - (2.7 cm/s^2)(4.0 s)^2 = 32.4 cm - 43.2 cm = -10.8 cm
Therefore, the displacement of the mouse in the interval from t=0 to t=4.0 is:
Displacement = Final position - Initial position = (-10.8 cm) - 0 cm = -10.8 cm
Average velocity = Displacement / Time interval = (-10.8 cm) / 4.0 s = -2.7 cm/s
So the average velocity of the mouse in the interval from t=0 to t=4.0 is -2.7 cm/s.
Therefore, the answers are:
A) Average velocity = 2.7 cm/s
B) Average velocity = -2.7 cm/s