An object is dropped from rest.
What is its instantaneous speed when it has
been in motion for 8 s? The acceleration of
gravity is 9.8 m/s2 .
Answer in units of m/s
To find the instantaneous speed of an object that has been in motion for 8 seconds when dropped from rest, we need to use the equation for the displacement of an object under constant acceleration.
The equation we will use is:
s = ut + 0.5at^2
Where:
s = displacement (unknown)
u = initial velocity (0 m/s, as the object is dropped from rest)
a = acceleration (acceleration due to gravity = 9.8 m/s^2)
t = time (8 s)
We can rearrange the equation to solve for the unknown, s:
s = 0.5at^2
Now we can substitute the known values into the equation:
s = 0.5 * 9.8 * (8)^2
Simplifying this equation:
s = 0.5 * 9.8 * 64
s = 313.6 m
The displacement of the object after 8 seconds of motion is 313.6 meters.
To find the instantaneous speed, we can use another equation:
v = u + at
Where:
v = final velocity or instantaneous speed (unknown)
u = initial velocity (0 m/s)
a = acceleration (9.8 m/s^2)
t = time (8 s)
Substituting the known values into the equation:
v = 0 + 9.8 * 8
v = 78.4 m/s
Therefore, the instantaneous speed of the object after being in motion for 8 seconds is 78.4 m/s.
V(t) = g*t
where
g = 9.8 m/s^2