187500 Joules of work must be done to the 3000 kg car to change its speed from 10 m/s to 15 m/s.
Explanation:
Work is the measurement of the force on an object that overcomes a resisting force (such as friction or gravity) times the distance the object is moved. If there is no distance, there is no work, no matter what the effort.
Work done = Force * displacement
When you apply enough force on an object to overcome a resistive force, such that you move that object, you are doing work on that object. There is a relationship between that work and mechanical energy.
When an object is accelerated, you are doing work against inertia, such that the work equals the change in kinetic energy of the object.
Work done = Change in K.E
In the given case:
mass = m = 3000 kg
initial velocity = v₁ = 10 m/s
final velocity = v₂ = 10 m/s
Work = W = (1/2)m(v₂)² - (1/2)m(v₁)²
[tex]= \frac{1}{2}m(v2^{2} - v1^2)\\= \frac{3000}{2}(15^{2} - 10^{2})\\= 1500(225 - 100)\\= 1500*125\\= 187500 kg m^{2}s^{-2} \\= 187500 Nm\\= 187500 J[/tex]
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