Kiriari is a market center from kisumu town a bus starts from kisumu for kiriari at 7:00am at an average speed of 80km/h at8:30am a car in stead from kisumu to kiriari and moved at an average speed of 120km/h
A)the distance bus covered before the car started moving
B)the relative speed for the vehicles
C)the time the car overtook the bus
D)the distance covered by the car before overtaking the bus
2)a car travels from rest to a velocity of 10km/h in 10seconds it travelled at this velocity for 20seconds and then came to stop in 5seconds find the initial acceleration
B)the distance travelled
A) To find the distance the bus covered before the car started moving, we need to calculate the time it took for the car to start moving.
The bus started at 7:00 am and the car started at 8:30 am. There is a time difference of 1 hour and 30 minutes, which is equal to 1.5 hours.
The bus traveled for 1.5 hours at an average speed of 80 km/h.
Distance covered = Speed × Time
Distance covered = 80 km/h × 1.5 hours
Distance covered = 120 km
Therefore, the bus covered a distance of 120 km before the car started moving.
B) The relative speed of the vehicles is the difference in their speeds.
Relative speed = Speed of car - Speed of bus
Relative speed = 120 km/h - 80 km/h
Relative speed = 40 km/h
Therefore, the relative speed of the vehicles is 40 km/h.
C) To find the time the car overtook the bus, we need to calculate the time it took for the car to cover the distance that the bus covered before.
The distance covered by the bus before the car started moving is 120 km.
Time taken by the car to cover the same distance = Distance ÷ Speed
Time taken by the car = 120 km ÷ 120 km/h
Time taken by the car = 1 hour
Therefore, the car overtook the bus after 1 hour.
D) The distance covered by the car before overtaking the bus is the distance covered in 1 hour.
Distance covered by the car = Speed × Time
Distance covered by the car = 120 km/h × 1 hour
Distance covered by the car = 120 km
Therefore, the car covered a distance of 120 km before overtaking the bus.
2) To find the initial acceleration, we can use the formula:
Final velocity = Initial velocity + (Acceleration × Time)
The final velocity is 10 km/h, the initial velocity is 0 km/h (since the car starts from rest), and the time taken is 10 seconds.
10 km/h = 0 km/h + (Acceleration × 10 seconds)
Rearranging the equation:
10 km/h = 10 seconds × Acceleration
Dividing both sides by 10 seconds:
Acceleration = 1 km/h / 10 seconds
Since the initial acceleration is usually expressed in m/s², we need to convert km/h to m/s.
1 km/h = 1000 m / 3600 s = 1000/3600 m/s = 1/3.6 m/s
Therefore:
Acceleration = (1/3.6) m/s / 10 seconds
Acceleration = 1/36 m/s²
Therefore, the initial acceleration is 1/36 m/s².
B) To find the distance travelled, we can use the formula:
Distance = (Initial velocity × Time) + (0.5 × Acceleration × Time²)
The initial velocity is 10 km/h, the time taken at this velocity is 20 seconds, and the acceleration is 0 m/s² (since the car came to a stop).
Distance = (10 km/h × 20 seconds) + (0.5 × 0 m/s² × (20 seconds)²)
Distance = (10 km/h × 20 seconds) + 0 m
Distance = 200 km
Therefore, the distance travelled by the car is 200 km.
A) To find the distance the bus covered before the car started moving, we can determine the time it took for the car to start moving after the bus started.
The bus started at 7:00 am and the car started at 8:30 am. The time difference is 1 hour 30 minutes, which is equal to 1.5 hours.
Distance covered by the bus = speed * time
Distance = 80 km/h * 1.5 hours
Distance = 120 km
Therefore, the bus covered a distance of 120 km before the car started moving.
B) The relative speed between the vehicles can be found by subtracting the speeds of the two vehicles.
Relative speed = Speed of car - Speed of bus
Relative speed = 120 km/h - 80 km/h
Relative speed = 40 km/h
Therefore, the relative speed between the vehicles is 40 km/h.
C) To find the time it took for the car to overtake the bus, we need to find the time difference between when the car started and when it caught up to the bus.
The car started at 8:30 am, and we need to find the time it took to catch up to the bus.
Since the car's speed is faster than the bus, it will catch up to the bus at some point. The time it took for the car to catch up to the bus is the same as the time it took for the car to travel the distance covered by the bus.
Time taken by the car to reach the distance covered by the bus = Distance / Speed
Time = 120 km / 120 km/h
Time = 1 hour
Therefore, the car overtook the bus in 1 hour.
D) To find the distance covered by the car before overtaking the bus, we can use the time it took for the car to catch up to the bus.
Distance covered by the car = Speed * Time
Distance = 120 km/h * 1 hour
Distance = 120 km
Therefore, the car covered a distance of 120 km before overtaking the bus.
2) To find the initial acceleration of the car:
Given:
Initial velocity (u) = 0 km/h (because the car starts from rest)
Final velocity (v) = 10 km/h
Time taken (t) = 10 seconds
Acceleration (a) = ?
Using the formula:
Acceleration (a) = (v - u) / t
Substituting the given values:
Acceleration (a) = (10 km/h - 0 km/h) / 10 seconds
Acceleration (a) = 1 km/h/s
Therefore, the initial acceleration of the car is 1 km/h/s.
To find the distance travelled:
Given:
U = 0 km/h
V = 10 km/h
Time taken (t) = 20 seconds (as the car travels at this velocity for 20 seconds)
Using the formula:
Distance (S) = (u + v) / 2 * t
Substituting the given values:
Distance (S) = (0 km/h + 10 km/h) / 2 * 20 seconds
Distance (S) = 5 km/h * 20 seconds
Distance (S) = 100 km
Therefore, the distance travelled by the car is 100 km.