Question

A stone of mass 2 kg is changing its velocity from 3 m/s to 18 m/'s in 15 s. The change
in KE, power delivered and force acted on the stone

Answer 1

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Change in K. E = Increase by 315J

Force on body = 2N

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It is given that ---------->

Mass of stone = 2kg

Since it changes ita velocity from 3m/s to 18m/s

Thus, Initial velocity of stone = u = 3m/s

Final velocity of stone v = 18m/s

Time it takes to change velocity = 15s.

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Now for a body it's kinetic energy is half of the product of it's mass and square of it's velocity.

Mathematically kinetic energy of a body is represented by --->

$\frac{1}{2} \times m {v}^{2}$

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Now change in kinetic energy of this stone

= Final kinetic energy - Initial kinetic energy

Now final kinetic energy of stone

=1/2 × m× final velocity^2

$\frac{1}{2} \times 2 \times {18}^{2}$

$= 1 \times {18}^{2}$

$= 324joules$

Now initial kinetic energy of stone

= 1/2 × m × initial velocity^2

$\frac{1}{2} \times 2 \times {3}^{2}$

$= 1 \times {3}^{2}$

$= 9joules$

Now change in kinetic energy = 324 - 9

=315 joules.

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Now acceleration of a body is defined as the rate of change of velocity.

Final velocity of stone = 18m/s

Initial velocity of stone = 3m/s

Time taken to accelerate = 15s

Therefore acceleration =

$\frac{v-u}{t}$

$\frac{18-3}{15}$

$= \frac{15}{15}$

$= 1m/ {s}^{2}$

Since force on a body is product of mass and acceleration.

Thus force on this body is

2×1

$= 2newton$

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BY SCIVIBHANSHU

THANK YOU

STAY CURIOUS

Answer 2

We have,

Mass of object = 2 kg

Initial velocity = 3 m/s

Final velocity = 18 m/s

1. Change in Kinetic energy = ½m(v + u)(v - u)

⇒Change in K.E. = ½ × 2 kg(18 m/s + 3 m/s)(18 m/s - 3 m/s)

= 1 kg × (21 m/s)(15 m/s)

= 315 Nm

⇒Change = 315 J

2. We know,

F = m(v - u)/t {Rate of change of 'p'}

⇒F = 2 kg(18 m/s - 3 m/s)/15 s

⇒F = 2 kg(15 m/s)/15 s

⇒F = 2 kg × 1 m/s²

⇒F = 2 N