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

Question

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

Answer 1

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.