Question

The velocity of a body of mass 5 kg acted upon by a constant retarding force of 10 N reduces to half of its initial value in 2 seconds, then initial velocity of the body is 3 m/s o 8 m/s 12 m/s 14.5 m/s​

Answer 1

Answer :-

Initial velocity of the body is 8 m/s .

Explanation :-

We have :-

→ Mass of the body (m) = 5 kg

→ Force acting (F) = 10 N

→ Time taken (t) = 2 sec

________________________________

Let the initial velocity of the body be u m/s . Then final velocity of the body will be u/2 m/s as it reduces to half of it's initial value .

Also as the force acting is a retarding force, so it's value will be -10 N .

________________________________

Finally, putting values in Newton's 2nd law of motion, we get :-

F = m(v - u)/t

⇒ -10 = 5(u/2 - u)/2

⇒ -10(2) = 5u/2 - 5u

⇒ -20 = (5u - 10u)/2

⇒ -20(2) = -5u

⇒ -40 = -5u

⇒ u = -40/-5

⇒ u = 8 m/s

Answer 2

Answer:

• Initial velocity (u) = 8 m/s

Explanation:

Given information,

The velocity of a body of mass 5 kg acted upon by a constant retarding force of 10 N reduces to half of its initial value in 2 seconds, then initial velocity of the body is?

• Mass (m) = 5 kg
• Force (F) = 10 N
• Time taken (t) = 2 seconds
• Initial velocity (u) = ?

Now, let's find acceleration (a) by using first equation of motion. We clearly know that it is given by;

• v = u + at

➻ v - u = at

➻ (v - u)/t = a

➻ a = (v - u)/t

• Hence, acceleration is (v - u)/t m/s².

Now, let's find its initial velocity (u) by using Newton's second law of motion. We clearly know that it is given by;

• F = ma

Here, given force is retarding so its value will be in negative and we know that the velocity of a body to half of its initial value i.e, v = half of u. Therefore;

• Force (F) = -10 N
• Final velocity (v) = u/2 m/s

Putting all values,

➻ -10 = 5[(v - u)/t]

➻ -10 = 5 × (u/2 - u)/2

➻ -10 = 5 × (u/2 - 2u/2)/2

➻ -10 = 5 × [(u - 2u)/2]/2

➻ -10 = 5 × (-u/2)/2

➻ -10 = 5 × -u/2 ÷ 2

➻ -10 = 5 × -u/2 × 1/2

➻ -10 = 5 × (-u × 1)/(2 × 2)

➻ -10 = 5 × -u/4

➻ -10 ÷ 5 = -u/4

➻ -10/5 = -u/4

➻ -2 = -u/4

➻ -2 × 4 = -u

➻ -8 = -u

➻ 8 = u

➻ u = 8

• Hence, initial velocity is 8 m/s.

Important definitions,

• Mass

Weight or quantity of matter in any object is known as mass.

• Force

A push or pull applied on an object is known as force.

• Acceleration

Acceleration is the process where velocity changes. Since, velocity is the speed and it has some direction. So, change in velocity is considered as acceleration.

• Initial velocity

Initial velocity is the velocity of the object before the effect of acceleration.

• Final velocity

After the effect of acceleration, velocity of the object changes. The new velocity gained by the object is known as final velocity.

▬▬▬▬▬▬▬▬▬▬▬▬