An Australian emu is running due north in a straight line at a speed of 13.0 m/s and slows down to a speed of 10.9 m/s in 2.20 s. Assuming that the acceleration of the bird remains the same, how far the bird will travel before it comes to a full stop?
the deceleration is
... (13.0 -10.9) m/s / 2.20 s
... slightly less than 1 m/s^2
so it takes about 13 s to stop
... during which the average speed is
... (13.0 + 0) m/s / 2
To find the distance the emu will travel before coming to a full stop, we need to determine the acceleration of the bird first. We can use the formula:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 13.0 m/s, the final velocity (v) is 10.9 m/s, and the time (t) is 2.20 s, we can substitute these values into the formula:
acceleration = (10.9 m/s - 13.0 m/s) / 2.20 s
Simplifying the equation:
acceleration = (-2.1 m/s) / 2.20 s
acceleration = -0.95 m/s²
The negative sign indicates that the emu is decelerating.
Now, we can use the equation of motion to find the distance (d) the emu will travel before coming to a full stop:
d = (v² - u²) / (2 * acceleration)
Substituting the values into the equation:
d = (0 m/s - 13.0 m/s) / (2 * (-0.95 m/s²))
Simplifying the equation:
d = (-13.0 m/s) / (-1.90 m/s²)
d = 6.84 m/s²
Therefore, the emu will travel approximately 6.84 meters before coming to a full stop.