Sally the bug has an initial speed of 20.0cm/s. She then accelerates at 8.00cm/s^2 for 5.00s.
calculate sallys total displacement? which i did and got 200 cm
Displacement during the 5th second?
can you please help and show all work
To calculate Sally's displacement during the 5th second, we need to know her initial speed and acceleration.
Given:
Initial speed, u = 20.0 cm/s
Acceleration, a = 8.00 cm/s^2
Time, t = 5.00 s
We can use the formula for displacement, which is:
Displacement (s) = ut + (1/2)at^2
In this case, we want to find the displacement during the 5th second, which means we need to calculate the displacement between the times t = 4 seconds and t = 5 seconds.
First, let's calculate the displacement from t = 0 to t = 4 seconds using the formula:
s = ut + (1/2)at^2
Substituting the values:
u = 20.0 cm/s
t = 4.00 s
a = 8.00 cm/s^2
s = (20.0 cm/s)(4.00 s) + (1/2)(8.00 cm/s^2)(4.00 s)^2
s = 80.0 cm + (1/2)(8.00 cm/s^2)(16.0 s^2)
s = 80.0 cm + 64.0 cm
s = 144.0 cm
Now, let's calculate the displacement from t = 0 to t = 5 seconds using the same formula:
s = ut + (1/2)at^2
Substituting the values:
u = 20.0 cm/s
t = 5.00 s
a = 8.00 cm/s^2
s = (20.0 cm/s)(5.00 s) + (1/2)(8.00 cm/s^2)(5.00 s)^2
s = 100.0 cm + (1/2)(8.00 cm/s^2)(25.0 s^2)
s = 100.0 cm + 100.0 cm
s = 200.0 cm
Now, to find the displacement during the 5th second, we subtract the displacement at t = 4 seconds from the displacement at t = 5 seconds:
Displacement (5th second) = Displacement (t = 5 s) - Displacement (t = 4 s)
Displacement (5th second) = 200.0 cm - 144.0 cm
Displacement (5th second) = 56.0 cm
Therefore, Sally's displacement during the 5th second is 56.0 cm.