Question

A body accelerates uniformly from a speed 'u' to 'v' with an accekeration 'a' . if mass of the body is m,show that work done W is equal to 1/2 m (v square - u square ) pls answer this question I will mark brainliest​

Answer 1

Given :

• Initial speed = u
• Final speed = v
• Acceleration = a
• Mass = m
• Initial and final height/level from ground is same

To prove :

Work done (W) = (1/2)×mass×(speed)²

Formula used :

• Kinetic energy (KE) = (1/2)×mass × (speed)²
• Potential energy (PE) = mgh
• Work done = Change in energy

Solution :

☆ Initially

◕ Kinetic energy = KE = (1/2)×m×u²

◕ Potential energy = PE = mgh

◕ Initial Total energy = PE + KE = mgh + (1/2)mu²

☆ Finally

◕ Kinetic energy = KE = (1/2)×m×v²

◕ Potential energy = PE = mgh

◕ Final Total energy = PE + KE = mgh + (1/2)mv²

✪ Work done = Final total energy - Initial total energy

➠ W = { mgh + (1/2)mv² } - { mgh + (1/2)mu² }

➠ W = ( mgh - mgh ) + (1/2)mv² - (1/2)mu²

➠ W = (1/2) × m × (v² - u²)

Hence PROVED