Answer:
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
[tex]Average \ speed = \dfrac{Total \ distance}{Time}[/tex]
[tex]\therefore time, \, t = \dfrac{Total \ distance}{Average \ speed}[/tex]
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, [tex]v_{average}[/tex] = d/t
∴ [tex]v_{average}[/tex] = 80 km/1.5 hours = 53.[tex]\overline 3[/tex] km/h ≈ 53 km/h
The average speed of the truck for the total distance, [tex]v_{average}[/tex] ≈ 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
