Question

a body is moving with a speed of 10 metre per second on applying force of hundred Newton of mass 10 kg calculate acceleration energy and displacement​

Answer 1

Initially, A body is moving with initial velocity, u = 10 m/s . Mass of the body is m = 10 kg.

Suddenly, A force of 100 N is exerted against the body. We have to find:

(a) Acceleration

(b) Energy

(c) Displacement

(a)

Since, The force is acting against the motion of the body so it will be taken as negative.

Using the second law of motion,

⇒ F = m.a

⇒ -100 = 10 . a

⇒ a = -100/10

⇒ a = -10 m/s²

So, The acceleration will be -10m/s². Negative sign here, indicates that it is deceleration.

(b)

We have,

Initial velocity, u = 10 m/s

Mass, m = 10 kg

Using Kinetic energy formula,

⇒ K.E = 1/2.m.u²

⇒ K.E = 1/2 . 10 . (10)²

⇒ K.E = 5 . 100

⇒ K.E = 500 J

Hence, The Energy (Only Kinetic Energy) of the body is 500 J.

(c)

Here, we have to find the displacement.

Due to deceleration (negative acceleration) the body will surely come to rest after some time.

So, Here we have to find the distance travelled by the body before coming to rest.

According to Work-Energy theorem, the work done on the body is equal to change in its kinetic energy.

So,

⇒ Work Done = Force . Displacement

⇒ (Final energy - Initial energy) = -100 . Displacement

⇒ Displacement = (0 - 500)/-100

⇒ Displacement = -500/-100

⇒ Displacement = 5 m

Hence, The displacement of the body will be 5 m.

Note:-

The final energy is taken as 0. because the velocity of the body will be 0 at rest hence the kinetic energy will also be 0.

Answer 2

ANSWER

$\LARGE{\red{\boxed{\purple{\underline{\blue{\underline{ \green{ \underline{\orange{\mathtt{Answer:↓}}}}}}}}}}}$

$\LARGE\bold{ \red{ \boxed{\blue{\underline{\mathtt{\red{Given- that:↓}}}}}}}$

• Initially, A body is moving with initial velocity,

$u = 10 m/s .$

${Mass \: of \: the \: body \: is \: m = 10 kg}$

$\sf \bf {\boxed {\mathbb {Suddenly}}}$

,

• A force of 100 N is exerted against the body. We have to find:.
• $\LARGE\bold{ \purple{ \boxed{\blue{\underline{\mathtt{\purple{ Acceleration:↓}}}}}}}$
• $\LARGE\bold{ \purple{ \boxed{\blue{\underline{\mathtt{\purple{ Energy↓}}}}}}}$
• $\LARGE\bold{ \purple{ \boxed{\blue{\underline{\mathtt{\purple{Displacement↓}}}}}}}$

$\LARGE\bold{ \red{ \boxed{\red{\underline{\blue{\underline{\green{\underline{\mathtt{\blue{Explanation↓}}}}}}}}}}}$

(a)$\LARGE\bold{ \green{ \boxed{\blue{\underline{\mathtt{\green{A:↓}}}}}}}$

• Since, The force is acting against the motion of the body so it will be taken as negative.

$\LARGE{\red{\boxed{\purple{\underline{\blue{\underline{ \green{ \underline{\orange{\mathtt{we-know-that:↓}}}}}}}}}}}$

• Using the second law of motion,

1. ⇒ F = m.a
2. ⇒ -100 = 10 . a
3. ⇒ a = -100/10
4. ⇒ a = -10 m/s².

$\LARGE\bold{ \red{ \boxed{\blue{\underline{\mathtt{\red{Now:↓}}}}}}}$

• So, The acceleration will be -10m/s². Negative sign here, indicates that it is deceleration.

(b)$\LARGE\bold{ \green{ \boxed{\blue{\underline{\mathtt{\green{B:↓}}}}}}}$

We have,

Initial velocity, u = 10 m/s

Mass, m = 10 kg

$\LARGE\bold{ \red{ \boxed{\blue{\underline{\mathtt{\red{Formula↓}}}}}}}$

Using Kinetic energy formula,

⇒ K.E = 1/2.m.u²

⇒ K.E = 1/2 . 10 . (10)²

⇒ K.E = 5 . 100

⇒ K.E = 500 J

$\LARGE\bold{ \orange{ \boxed{\blue{\underline{\mathtt{\orange{Therefore↓}}}}}}}$

Hence, The Energy (Only Kinetic Energy) of the body is 500 J.

(c)$\LARGE\bold{ \green{ \boxed{\blue{\underline{\mathtt{\green{C:↓}}}}}}}$

• Here, we have to find the displacement.
• Due to deceleration (negative acceleration) the body will surely come to rest after some time.

So, Here we have to find the distance travelled by the body before coming to rest.

According to Work-Energy theorem, the work done on the body is equal to change in its kinetic energy.

$\sf \bf \huge {\boxed {\mathbb {INFORMATION}}}$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

So,

⇒ Work Done = Force . Displacement

⇒ (Final energy - Initial energy) = -100 . Displacement

⇒ Displacement = (0 - 500)/-100

⇒ Displacement = -500/-100

⇒ Displacement = 5 m

Hence, The displacement of the body will be 5 m.

$\sf \bf {\boxed {\mathbb {NOTE}}}$

The final energy is taken as 0. because the velocity of the body will be 0 at rest hence the kinetic energy will also be 0.