Question

how does the work required to accelerate a particle from 10 m/s to 20 m/s compare to that required to accelerate it from 20 m/s to 30 m/s ? responses it is less. it is less. it is the same. it is the same. it is greater. it is greater. it cannot be determined without knowing the magnitude of the force exerted on the particle. it cannot be determined without knowing the magnitude of the force exerted on the particle. it cannot be determined without knowing the mass of the particle.

Answer 1

More work is required to accelerate a particle from 20 m/s to 30 m/s than from 10 m/s to 20 m/s, as deduced by comparing the changes in kinetic energy for each interval, which shows a greater change for the second interval.

Step-by-step explanation:

The work required to accelerate a particle with a constant mass from 10 m/s to 20 m/s as compared to accelerating it from 20 m/s to 30 m/s can be determined using the work-energy theorem. This theorem states that the work done on an object is equal to the change in its kinetic energy. The kinetic energy (KE) of an object is given by the formula KE = (1/2)mv2, where m is mass and v is velocity.

For the same mass, the change in kinetic energy (and hence the work done) can be calculated for each interval:

• Work from 10 m/s to 20 m/s: ∆KE = (1/2)m(202) - (1/2)m(102) = (1/2)m(400 - 100) = (1/2)m(300)
• Work from 20 m/s to 30 m/s: ∆KE = (1/2)m(302) - (1/2)m(202) = (1/2)m(900 - 400) = (1/2)m(500)

It is clear that more work is required to accelerate the particle from 20 m/s to 30 m/s than from 10 m/s to 20 m/s due to a greater change in kinetic energy in the former case. We do not need information about the force or the mass of the particle for this comparison, since the mass would cancel out when comparing the two intervals for the same particle.