Please help please real quick

1. (a) The final velocity is 20 m/s

(b) The distance travelled is20 meters

2. The distance travelled by the train in the 30 seconds is 825 meters

3. The most correct option is;

(d) 53 km

4. The heat, developed by the electric iron is 15,000 joules

5. a) In the first network the resistance between A and B is 2 Ω

b) In the second network the resistance between A and B is 4Ω

c) In the third network the resistance between A and B is 6Ω

d) In the fourth network the resistance between A and B is 2Ω

Explanation:

1. (a) The parameters of the cheetahs motion are;

The initial motion (velocity) of the cheetah = 0 m/s (The cheetah starts from rest)

The acceleration of the cheetah, a = 2 m/s²

The duration of the acceleration of the cheetah, t = 10 seconds

The kinematic equation of the motion of uniform acceleration, of the cheetah can be written in the following form;

v = u + a·t

s = u·t + 1/2·a·t²

Where;

v = The final velocity

u = The initial velocity = 0 m/s

a = The acceleration of the cheetah = 2 m/s²

s = The distance traveled

∴ v = 0 + 2 × 10 = 20

The final velocity, v = 20 m/s

(b) From s = u·t + 1/2·a·t², we have;

s = 0 × 10 + 1/2 × 10 × 2² = 20

The distance travelled, s = 20 meters

2. The given details of the motion of the train are;

The initial velocity of the train, u = 20 m·s⁻¹

The acceleration of the train, a = 0.5 m·s⁻²

The duration of the train's acceleration, t = 30 seconds

Therefore, the distance travelled, 's', is given by; s = u·t + 1/2·a·t²

∴ s = 20 × 30 + (1/2) × 0.5 × 30² = 825

The distance travelled by the train in the 30 seconds, s = 825 meters

3. The given distance the truck covers with the average speed of 80 km/h, d₁ = 40 km

The distance the truck then covers with the average speed of 40 km/h, d₂ = 40 km

The time it takes the truck to cover the 40 km at 80 km/h = 40 km/(80 km·h) t₁ = 0.5 hour

The time it takes the truck to cover the 40 km at 80 km/h = 40 km/(40 km·h) t₂ = 1 hour

The total time taken to cover both 40 km distances, t = t₁ + t₂

∴ The total time taken to cover both 40 km distances, t = (0.5 + 1) hour = 1.5 hours

The total distance covered at both speeds, d = d₁ + d₂

∴ d = 40 km + 40 km = 80 km

The average speed of the truck for the total distance, = d/t

∴ = 80 km/1.5 hours = 53. km/h ≈ 53 km/h

The average speed of the truck for the total distance, ≈ 53 km/h

The correct option is (d) 53 km

4. The heat, 'H', developed by the electric iron is given by the following formula;

H = I²·R·t

Where;

I = The current flowing in the electric iron = 5 A

R = The resistance of the iron = 20Ω

t = The time duration of the flow of the current = 30 s

∴ H = (5 A)² × 20 Ω × 30 s = 15,000 joules

The heat, developed by the electric iron, H = 15,000 joules

5. Let 'R' represent the resistance between A and B in each network

a) For the first network, we have;

1/R = 1/(2 + 2) + 1/(2 + 2) = 1/4 + 1/4 = 1/2

∴ R = 2 Ω

∴ The resistance between A and B is 2 Ω

b) For the second network, we have;

R = 1/(1/2 + 1/2) + 3 = 4

R = 4Ω

∴ The resistance between A and B is 4 Ω

c) For the third network, we have;

R = 2 + 1/(1/4 + 1/4) + 2 = 6

R = 6Ω

∴ The resistance between A and B is 6 Ω

d) For the fourth network, we have;

R = 1/(1/2 + 1/2) + 1/(1/2 + 1/2) = 2

R = 2Ω

∴ The resistance between A and B is 2 Ω

newton's first law of motion

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