To find the acceleration of the dog, we need to use the following formula:
a = (v_f - v_i) / t
Where:
a = acceleration
v_f = final velocity
v_i = initial velocity
t = time
In this case, the initial velocity (v_i) of the dog is 1.23 m/s to the east (positive direction) and the final velocity (v_f) is unknown. The displacement (d) of the dog is 34.3 m to the east (positive direction) and the time (t) taken to travel this distance is 7.3 s.
We can use the formula for displacement to find the final velocity:
d = (v_f + v_i) / 2 * t
Rearranging this formula to solve for v_f, we get:
v_f = (2 * d / t) - v_i
Substituting the given values, we get:
v_f = (2 * 34.3 m / 7.3 s) - 1.23 m/s
v_f = 4.04 m/s
Now we can substitute the values of v_f, v_i, and t into the formula for acceleration:
a = (v_f - v_i) / t
a = (4.04 m/s - 1.23 m/s) / 7.3 s
a = 0.410 m/s^2 [E]
Therefore, the acceleration of the dog is 0.410 m/s^2 to the east (positive direction).