High School

1. Solve the following numerical problems:

a. If a car is moving with the speed of 36 km/hr, convert it into m/s. [Ans: 10 m/s]

b. If a car travels a distance of 900 m in 30 seconds, what will be the speed of the car? [Ans: 30 m/s]

c. The velocity of a taxi increases from 5 m/s to 20 m/s in 15 seconds, what will be the acceleration of the taxi? [Ans: 1 m/s²]

d. A bus is moving with a speed of 10 m/s. How much distance does it travel in 20 seconds? [Ans: 200 m]

e. A man throws a stone of mass 3 kg and the stone falls down 500 metres away from him. What is the work done by him? [Ans: 15000 J]

f. If a worker moves a mass of 60 kg through 300 metres in 1 minute, what is the power? [Ans: 3000 Watt]

g. A man of weight 450 N carries a weight of 150 N and climbs up a ladder through a height of 3 meters in 10 seconds. What is his power? [Ans: 180 Watt]

Answer :

Let's solve these numerical problems step-by-step:

  1. Convert speed from km/hr to m/s:

    • Given speed: 36 km/hr
    • To convert km/hr to m/s, use the conversion factor: [tex]1 \text{ km/hr} = \frac{1}{3.6} \text{ m/s}[/tex].
    • [tex]36 \times \frac{1}{3.6} = 10 \text{ m/s}[/tex].

  2. Find the speed of the car:

    • Distance traveled: 900 meters
    • Time taken: 30 seconds
    • Speed = [tex]\frac{\text{distance}}{\text{time}} = \frac{900}{30} = 30 \text{ m/s}[/tex].

  3. Calculate the acceleration of the taxi:

    • Initial velocity: 5 m/s
    • Final velocity: 20 m/s
    • Time taken: 15 seconds
    • Acceleration = [tex]\frac{\text{change in velocity}}{\text{time}} = \frac{20 - 5}{15} = 1 \text{ m/s}^2[/tex].

  4. Calculate distance traveled by the bus:

    • Speed of the bus: 10 m/s
    • Time: 20 seconds
    • Distance = [tex]\text{speed} \times \text{time} = 10 \times 20 = 200 \text{ meters}[/tex].

  5. Calculate the work done by a man throwing a stone:

    • Mass of the stone: 3 kg
    • Distance: 500 meters
    • Since work done = weight [tex]\times[/tex] distance, and weight [tex]= \text{mass} \times \text{gravity} = 3 \times 10 = 30 \text{ N}[/tex],
    • Work = [tex]30 \times 500 = 15000 \text{ J}[/tex] (assuming gravity [tex]g = 10 \text{ m/s}^2[/tex]).

  6. Calculate power for moving a mass:

    • Mass: 60 kg
    • Distance: 300 meters
    • Time: 1 minute (60 seconds)
    • Power is [tex]\frac{\text{Work}}{\text{Time}}[/tex] and Work = Weight [tex]\times[/tex] distance
    • Weight = [tex]60 \times 10 = 600 \text{ N}[/tex]
    • Work = [tex]600 \times 300 = 180000 \text{ J}[/tex]
    • Power = [tex]\frac{180000}{60} = 3000 \text{ Watts}[/tex].

  7. Find power exerted by a man climbing a ladder:

    • Total weight carried: 450 N + 150 N = 600 N
    • Height: 3 meters
    • Time: 10 seconds
    • Power = [tex]\frac{\text{Work}}{\text{Time}}[/tex] where Work = Weight [tex]\times[/tex] height
    • Work = [tex]600 \times 3 = 1800 \text{ J}[/tex]
    • Power = [tex]\frac{1800}{10} = 180 \text{ Watts}[/tex].

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