Answer:
<h2>0.245cm/min</h2>
Explanation:
The volume of the spherical balloon is expressed as V = 4/3πr³ where r is the radius of the spherical balloon. If the spherical balloon is inflated with gas at the rate of 500 cubic centimetres per minute then dV/dt = 500cm³.
Using chain rule to express dV/dt;
dV/dt = dV/dr*dr/dt
dr/dt is the rate at which the radius of the gallon is increasing.
From the formula, dV/dr = 3(4/3πr^3-1))
dV/dr = 4πr²
dV/dt = 4πr² *dr/dt
500 = 4πr² *dr/dt
If radius r = 40;
500 = 4π(40)² *dr/dt
500 = 6400π*dr/dt
dr/dt = 500/6400π
dr/dt = 5/64π
dr/dt = 0.245cm/min
Hence, the radius of the balloon is increasing at the rate of 0.245cm/min
The average acceleration of the car as it accelerates from 15 m/s to 25 m/s will be 2.5 m/s².
<h3>What is Average acceleration?</h3>
Average acceleration is the average rate of change of velocity with respect to time. Mathematically -
a = Δv/Δt
Given that a car is traveling at 15 m/s in north direction and in 4 seconds it accelerates to 25 m/s in the north direction only. Therefore, we can write -
initial velocity [u] = 15 m/s
final velocity [v] = 25 m/s
time taken [Δt] = 4 s
The magnitude of the average acceleration can be calculated as follows-
a = Δv/Δt
Δv = v - u = 25 - 15
Δv = 10 m/s
Therefore -
a = 10/4
a = 2.5 m/s².
Therefore, the average acceleration of the car will be 2.5 m/s².
To solve more questions on Acceleration, visit the link below-
brainly.com/question/21300541
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