An automobile accelerates from rest at

1.3 m/s
2
for 19 s. The speed is then held
constant for 23 s, after which there is an acceleration of −0.9 m/s
2
until the automobile
stops.
What total distance was traveled?
Answer in units of km

I need help finding Vfinal. I have Vinitial, acceleration, and distance.

To find the total distance traveled, we need to calculate the distance covered during each phase of the motion and then sum them up.

Phase 1: Acceleration from rest to a constant speed.
We can use the equation of motion: d = (1/2) * a * t^2, where d is the distance covered, a is the acceleration, and t is the time.
Given:
Acceleration, a = 1.3 m/s^2
Time, t = 19 s

Using the formula, d = (1/2) * 1.3 * (19)^2

Phase 2: Constant speed.
Since the speed is held constant, the distance covered can be calculated using the formula: d = v * t, where v is the constant velocity and t is the time.
Given:
Constant velocity, v (which is the same as the final velocity in phase 1)
Time, t = 23 s

Using the formula, d = v * 23

Phase 3: Deceleration from the constant speed to stop.
The initial velocity for this phase is the same as the final velocity of phase 2.
Given:
Deceleration, a = -0.9 m/s^2
Time, t is not given, but we can calculate it since we know the displacement is zero at the end of this phase.

Using the formula, v = u + a * t (where u is the initial velocity, v is the final velocity, a is the acceleration, and t is the time),
0 = v + (-0.9) * t (since the automobile stops, the final velocity is 0)
Solving for t, t = v / 0.9

Now, we have the time for phase 3. We can calculate the distance using the equation of motion: d = (1/2) * (v + u) * t, where v is the final velocity, u is the initial velocity, and t is the time.
Given:
Initial velocity, u (which is the same as the constant velocity in phase 2)
Final velocity, v = 0 (since the automobile stops)
Time, t (calculated from the previous equation)

Using the formula, d = (1/2) * (0 + u) * t

Finally, to find the total distance traveled, we sum up the distances from all three phases:

Total Distance = Distance Phase 1 + Distance Phase 2 + Distance Phase 3

After calculating these distances, you can convert the answer to kilometers by dividing it by 1000 since there are 1000 meters in a kilometer.