Question

a car of mass 1000kg is moving with a velocity of 10 m/s.find the work needed to increase the speed from 10m/s to 25m/s​

Answer 1

Answer:

Here the given data is,

mass of the car = 1000 kg

initial velocity of the car = Vi = 10 m /sec.

final velocity of the car = Vf = 30 m / sec.

time required for this change in velocity = t= 10 sec.

power developed during this process = P = ?

by definition of Power ,

P = Work done / time ……………………(1)

first we find the work done,

From Work -Energy theorem we know that,

Work done = change in kinetic energy

Work done = 1/2 m Vf ˄2 – 1/2 m Vi˄2

= 1/2 m( Vf ˄2 – Vi˄2 )

= 1/2 x 1000 ( 30 ˄2 – 10˄2 )

= 500 ( 900 – 100 ) = 500 x 800 = 400000 j ……………(2)

Put this value of equation (2) in equation (1)

P = 400000 j / 10 sec. = 40000 watt. = 40 kW ……………answer

we can also calculate the power using the relation

Power = (applied force ) x ( average velocity of an object)

P=( F ) x (<V > ) …………….(1)

P =( m a) x (<V > )

P = m( Vf - Vi/t ) x ( Vf+ Vi/2 )

P = 1000 ( 30 - 10)/10 x ( 30+ 10)/2

P= 1000 (2) x 20

P= 40000 watt. = 40 kW ……………….answer

Explanation:

Hop it helps