An Australian emu is running due west in a straight line at a speed of 12.8 m/s and slows down to a speed of 7.7 m/s in 7.4 s. (a) What is the direction of the bird’s acceleration? (b) Assuming that the acceleration remains the same, what is the bird’s velocity after an additional 2.0 s has elapsed? (Assume that due west is the positive direction. Indicate the direction with the sign of your answer.)
a. if it slowed, the acceleration is opposite the velocity
b. vf=vi+at
vf=7.7-((7.7-12.8)/7.4 )* 2.0
+ answer means west, negative means E
a
east
b
v = Vi + a t = 12.8 -(7.7/7.4)9.4
To determine the direction of the bird's acceleration, we need to analyze the change in its velocity. Given that the bird is initially running due west and then slows down, we know that the acceleration will be in the opposite direction, which is east (or, in this case, the negative direction since we are using due west as the positive direction).
Now, let's calculate the magnitude of the bird's acceleration using the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (v₁) = 12.8 m/s
Final velocity (v₂) = 7.7 m/s
Time (t) = 7.4 s
Substituting the values:
acceleration = (7.7 m/s - 12.8 m/s) / 7.4 s
acceleration = (-5.1 m/s) / 7.4 s
acceleration = -0.689 m/s² (approximately)
Therefore, the bird's acceleration has a magnitude of 0.689 m/s² and is in the east (negative) direction.
To determine the bird's velocity after an additional 2.0 seconds have elapsed, we can use the equation:
v = v₀ + at
Given:
Initial velocity (v₀) = 7.7 m/s
Acceleration (a) = -0.689 m/s²
Time (t) = 2.0 s
Substituting the values:
v = 7.7 m/s + (-0.689 m/s²) * 2.0 s
v = 7.7 m/s - 1.378 m/s
v = 6.322 m/s (approximately)
The bird's velocity after an additional 2.0 seconds has elapsed is approximately 6.322 m/s, in the east (negative) direction.