Energy required to accelerate a car from rest to 10m/s:

To calculate the energy required to accelerate a car from rest to 10m/s, we can use the formula for kinetic energy:

Kinetic energy (KE) = 0.5 * mass * velocity^2

Given that the car is initially at rest, the initial velocity (u) is 0m/s, and the final velocity (v) is 10m/s. Therefore, the energy required to accelerate the car to 10m/s can be calculated as:

Energy (E) = KE (at v = 10m/s) - KE (at u = 0m/s)

Substituting the values into the formula, we get:

E = 0.5 * mass * (10^2 - 0^2)
E = 0.5 * mass * 100
E = 50 * mass

So, the energy required to accelerate the car from rest to 10m/s is 50 times the mass of the car.

Energy required to accelerate the car from 10m/s to 20m/s:

To find the energy required to accelerate the car from 10m/s to 20m/s, we can again use the formula for kinetic energy:

KE = 0.5 * mass * velocity^2

In this case, the initial velocity (u) is 10m/s, and the final velocity (v) is 20m/s. Therefore, the energy required to accelerate the car from 10m/s to 20m/s can be calculated as:

Energy (E) = KE (at v = 20m/s) - KE (at u = 10m/s)

Substituting the values into the formula, we get:

E = 0.5 * mass * (20^2 - 10^2)
E = 0.5 * mass * (400 - 100)
E = 0.5 * mass * 300
E = 150 * mass

So, the energy required to accelerate the car from 10m/s to 20m/s is 150 times the mass of the car.

Conclusion:

The energy required to accelerate a car from rest to 10m/s is 50 times the mass of the car, while the energy required to accelerate the same car from 10m/s to 20m/s is 150 times the mass of the car. This shows that the energy required for acceleration increases as the car's velocity increases. It is important to consider the energy requirements for acceleration when designing and operating vehicles to ensure efficient use of energy and optimize performance.