Let's break down the problem step by step:
a) To find the average velocity during each 2-second interval after passing the 92-ft point, we first need to determine the distance covered during each interval. The distances covered during the given time intervals are:
- 92 ft to 140 ft = 48 ft
- 140 ft to 198 ft = 58 ft
- 198 ft to 266 ft = 68 ft
Now, we find the average velocity using the formula: average velocity = total distance / total time
The total time for each interval is 2 seconds.
Average velocity from 92 ft to 140 ft: 48 ft / 2 sec = 24 ft/sec
Average velocity from 140 ft to 198 ft: 58 ft / 2 sec = 29 ft/sec
Average velocity from 198 ft to 266 ft: 68 ft / 2 sec = 34 ft/sec
b) To find the acceleration of the bus, we can use the formula for acceleration: acceleration = change in velocity / time
Acceleration from 92 ft to 140 ft: (24 ft/sec - 0) / 2 sec = 12 ft/sec^2
Acceleration from 140 ft to 198 ft: (29 ft/sec - 24 ft/sec) / 2 sec = 2.5 ft/sec^2
Acceleration from 198 ft to 266 ft: (34 ft/sec - 29 ft/sec) / 2 sec = 2.5 ft/sec^2
c) To find the velocity of the bus when it passed the 92-ft point, we can add up the average velocities:
Velocity at 140 ft = 24 ft/sec
Velocity at 198 ft = 24 ft/sec + 29 ft/sec = 53 ft/sec
Velocity at 266 ft = 53 ft/sec + 34 ft/sec = 87 ft/sec
d) To find the time it took to go from the station to the 92-ft point, we can use the formula: final velocity = initial velocity + acceleration * time
From 92 ft to 140 ft:
Final velocity = 24 ft/sec
Initial velocity = 0
Acceleration = 12 ft/sec^2
24 ft/sec = 0 + 12 ft/sec^2 * time
time = 24 ft/sec / 12 ft/sec^2 = 2 sec
So, the time it took to go from the station to the 92-ft point is 2 seconds.
A bus starts from rest at a station and runs with constant acceleration. The bus is 140 ft from the station 2 sec after passing a point which is 92 ft from the station. Four seconds after passing the 92-ft point, it is 198 ft from the station, and 6 sec after passing this point, it is 266 ft from the station.
a) What is the average velocity of the bus during each 2-sec interval after passing the 92-ft point?
b) What is the acceleration of the bus?
c) What was the velocity of the bus when it passed the 92-ft point?
d) How long did it take to go from the station to the 92-ft point?
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1 answer