Question

A body of mass 1kg is moving with 15m/s is stopped in 2sec . Calculate the impulse and opposing force.​

Answer 1

Answer:

• Opposing force = -7.5
• Impulse = 15 N

Explanation:

Given, A body of mass 1kg moving with a velocity of 15m/s comes at rest 2 seconds.

Calculate,

• Impulse.
• Opposing force.

Here,

the body comes to rest so final velocity (v) would be zero

Acceleration of the body,

→ a = (v - u)/t

Where,

• v denotes the final velocity
• u is the initial velocity = 15 m/s.
• t is the time = 2 sec

→ a = (0 - 15)/2

→ a = -15/2

→ a = -7.5

[Note: -ve sign denotes the against motion.]

Opposing force is given by,

→ F = m*a

Where,

• m is the mass of the body
• And, a is the acceleration.

→ F = 1*(-7.5)

→ F = -7.5

[Note: -ve sign denotes the opposite force.]

Now, Impulse of the body is given by,

Where,

• F is the force.
• t is time taken.

→ I = 7.5*2

→ I = 15.0

∴ Impulse of the body is 15 N

__________________________

$\:$

Answer 2

Answer:

Given :-

• A body of mass 1 kg is moving with 15 m/s is stopped in 2 seconds.

To Find :-

• What is the impulse and opposite force.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{v =\: u + at}}}\: \: \: \bigstar$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time Taken

$\clubsuit$ Force Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{F =\: m \times a}}}\: \: \: \bigstar$

where,

• F = Force
• m = Mass
• a = Acceleration

$\clubsuit$ Impulse Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Impulse =\: Force \times Time}}}\: \: \: \bigstar$

Solution :-

First, we have to find the acceleration :

Given :

• Final Velocity (v) = 0 m/s
• Initial Velocity (u) = 15 m/s
• Time Taken (t) = 2 seconds

According to the question by using the formula we get,

$\implies \bf v =\: u + at$

$\implies \sf 0 =\: 15 + a(2)$

$\implies \sf 0 =\: 15 + 2a$

$\implies \sf 0 - 15 =\: 2a$

$\implies \sf - 15 =\: 2a$

$\implies \sf \dfrac{- 15}{2} =\: a$

$\implies \sf - 7.5 =\: a$

$\implies \sf\bold{\blue{a =\: - 7.5\: m/s^2}}$

Hence, the acceleration is - 7.5 m/s² .

Now, we have to find the opposite force of a body :

Given :

• Mass (m) = 1 kg
• Acceleration (a) = - 7.5 m/s²

According to the question by using the formula we get,

$\implies \bf F =\: m \times a$

$\implies \sf Force =\: Mass \times Acceleration$

$\implies \sf Force =\: 1 \times (- 7.5)$

$\implies \sf\bold{\purple{Force =\: - 7.5\: N}}$

Hence, the opposite force of a body is - 7.5 N .

Now, we have to find the impulse :

Given :

• Force = 7.5 N
• Time = 2 seconds

According to the question by using the formula we get,

$\dashrightarrow \bf Impulse =\: Force \times Time$

$\dashrightarrow \sf Impulse =\: 7.5\: N \times 2\: s$

$\dashrightarrow \sf\bold{\red{Impulse =\: 15\: N\: s}}$

$\therefore$ The opposite force of a body is - 7.5 N and the impulse is 15 N s .

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