a bus starts from rest and in 30s it reaches speed of 20m/s.then the speed remains steady for 15s and decreases steadily until it stops 5s later.what the distance covered from strat to finish.
acceleration
... d = 30 s * [(20 m/s + 0 m/s) / 2]
cruise
... d = 15 s * 20 m/s
deceleration
... d = 5 s * [(20 m/s + 0 m/s) / 2]
add the three distances
To find the distance covered by the bus, we need to calculate the distance traveled during each phase of its motion and then sum them up.
Phase 1: Acceleration phase (0 to 20 m/s)
In this phase, the bus starts from rest and reaches a speed of 20 m/s in 30 seconds.
Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken, let's calculate the acceleration.
u = 0 m/s (initial velocity)
v = 20 m/s (final velocity)
t = 30 s (time taken)
v = u + at
20 = 0 + a * 30
a = 20 / 30
a = 0.67 m/s²
To find the distance covered during this phase, we can use the equation s = ut + (1/2) * a * t², where s is the distance traveled.
s = 0 * 30 + (1/2) * 0.67 * 30²
s = 0 + (1/2) * 0.67 * 900
s = 0 + 0.335 * 900
s = 301.5 meters
Phase 2: Constant speed (20 m/s) phase
During this phase, the bus maintains a steady speed of 20 m/s for 15 seconds. The distance covered can be calculated using the equation s = vt, where v is the constant velocity, and t is the time taken.
v = 20 m/s (constant velocity)
t = 15 s (time taken)
s = 20 * 15
s = 300 meters
Phase 3: Deceleration phase (20 to 0 m/s)
In this phase, the bus decreases its speed steadily until it comes to a stop.
Using the equation v = u + at, let's find the acceleration during this phase.
u = 20 m/s (initial velocity)
v = 0 m/s (final velocity)
t = 5 s (time taken)
v = u + at
0 = 20 + a * 5
-20 = 5a
a = -4 m/s²
To find the distance covered during this phase, we can again use the equation s = ut + (1/2) * a * t².
s = 20 * 5 + (1/2) * (-4) * 5²
s = 100 + (1/2) * (-4) * 25
s = 100 + (-50)
s = 50 meters
Now, we can find the total distance covered by adding up the distances from each phase.
Total distance = Phase 1 distance + Phase 2 distance + Phase 3 distance
Total distance = 301.5 + 300 + 50
Total distance = 651.5 meters
Therefore, the bus covered a distance of 651.5 meters from the start to the finish.
To find the distance covered from start to finish, we need to break down the motion of the bus into different intervals and calculate the distance covered in each interval separately.
First, let's calculate the distance covered during the acceleration phase. We know that the bus starts from rest and reaches a speed of 20 m/s in 30 seconds. This means we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the initial velocity is 0 and the acceleration is (change in velocity / time), we can calculate the distance covered during acceleration as follows:
distance_acceleration = (0.5 * (20 - 0) / 30 * 30^2)
Simplifying this equation gives us:
distance_acceleration = 0.5 * (20 / 30) * 900
distance_acceleration = 0.5 * (2/3) * 900
distance_acceleration = (1/3) * 900
distance_acceleration = 300 meters
Next, let's calculate the distance covered during the period of steady speed. The speed remains constant at 20 m/s for 15 seconds. Therefore, the distance covered during steady speed is:
distance_steady = speed * time
distance_steady = 20 * 15
distance_steady = 300 meters
Finally, let's find the distance covered during the deceleration phase. The bus takes 5 seconds to come to a stop, and the deceleration is equal to the initial velocity divided by time. Since the bus stops, the final velocity is 0, and the initial velocity is 20 m/s. Therefore, the distance covered during deceleration is:
distance_deceleration = (initial velocity * time) - (0.5 * acceleration * time^2)
Since the final velocity is 0, the acceleration is equal to (-initial velocity / time), and we can calculate the distance covered during deceleration as:
distance_deceleration = (20 * 5) - (0.5 * (20 / 5) * 5^2)
distance_deceleration = 100 - (0.5 * 4 * 25)
distance_deceleration = 100 - (2 * 25)
distance_deceleration = 100 - 50
distance_deceleration = 50 meters
Now, to find the total distance covered from the start to the finish, we add the distances covered during each phase:
total_distance = distance_acceleration + distance_steady + distance_deceleration
total_distance = 300 + 300 + 50
total_distance = 650 meters
Therefore, the bus covers a total distance of 650 meters from start to finish.