Answer:
C) Total displacement = 1275 m or 1.275 km
Step-by-step explanation:
We'll break this into two parts:
1) Displacement during constant speed, and
2) Displacement during the acceleration phase.
Constant Speed
The displacement for this segment is already stated: 1 km. But the information includes the time, which will allow us to calculate the speed of travel. We'll need this for the next phase of acceleration.
Distance = Speed x Time
Speed = Distance/Time
Time = 1 minute + 20 sec, or 80 sec.
Speed = 1 km/80 sec
Speed = 0.0125 km/sec
Since we'll be using meters (not km) in the next step, convert 0.0125 km/sec to m/sec with a conversion factor:
(0.0125 km/sec)*(1000m/1 km) = 12.5 m/sec
Acceleration Phase
The obect is moving at a speed of 12.5 m/sec (from above) and then accelerates at a rate of 0.125 m/sec^2 for 20 seconds.
The distance (s) an object travels during this acceleration (a) is gven by:
s = vi*t + (1/2)a*t^2,
where vi is the initial velocity (12.5 m/sec in this case), a is the acceleration (0.125 m/sec^2), and t is the time (20 seconds).
s = (12.5 m/sec)(20 sec) + (1/2)(0.125 m/sec^2)*(20 sec)^2
s = 275 meters
Now add the two distances:
1) Constant Speed Phase = 1000 m
2) Acceleration Phase = 275 m
Total displacement = 1275 m or 1.275 km