Question

A force of 0.4 N acts on a mass of 4 kg at rest. Calculate its velocity and momentum at the end of 10 s

Answer 1

Given :-

Mass of the object = 4 kg

Force acting on the object = 0.4 N

To Find :-

The velocity.

The momentum at the end of 10 s.

Analysis :-

Firstly, find the acceleration by substituting the given values in the formula of force.

Then, using the first equation of motion, you can easily get the final velocity required.

Finally, using the formula of momentum, you can substitute the values you got and find it accordingly.

Solution :-

We know that,

• u = Initial velocity
• a =  Acceleration
• m = Mass
• v = Final velocity
• p = Momentum
• t = Time
• f = Force

Using the formula,

$\underline{\boxed{\sf Force=Mass \times Acceleration}}$

Given that,

Force (f) = 0.4 N

Mass (m) = 4 kg

Substituting their values,

0.4 = 4 × a

a = 0.4/4

a = 0.1 m/s²

Using the formula,

$\underline{\boxed{\sf First \ equation \ of \ motion=v=u+at}}$

Given that,

Acceleration (a) = 0.1 m/s²

Time taken (t) = 10 sec

Initial velocity (u) = 0 m/s

Substituting their values,

v = 0 + 0.1 × 10

v = 0.1 × 10

v = 1 m/s

Therefore, the velocity is 1 m/s.

Using the formula,

$\underline{\boxed{\sf Momentum=Mass \times Final \ velocity}}$

Given that,

Mass (m) = 4 kg

Final velocity (v) = 1 m/s

Substituting their values,

p = 4 × 1

p = 4 kg m/s

Therefore, the momentum is 4 kg m/s.

Answer 2

Explanation:

Given :

• A force of 0.4 N acts on a mass of 4 kg at rest.

• time is 10 s

To Find :

• Calculate its velocity and momentum at the end of 10 s

Solution :

Concept :

• Momentum is a physics term; it refers to the quantity of motion that an object has.

• A sports team that is on the move has the momentum.

• If an object is in motion (on the move) then it has momentum.

•  Momentum can be defined as "mass in motion."

Momentum Calculator p = mv - Calculator Soup The Momentum Calculator uses the formula p = mv,

• momentum (p) is equal to mass (m) times velocity (v).

• The calculator can use any two of the values to calculate the third.

• According to the Formula :

$: \implies \: \: \: \boxed{ \sf \: a=\dfrac{F}{m}}$

• Substitute all values :

$: \implies \sf \: \: \: \: \: \: \: =\dfrac{0.4}{4} \\ \\ \\ : \implies\sf \: \: \: \: \: \: \: = 0.1 \ m/s^2$

We know,

Also, u (initial velocity) = 0 m/s.

$: \implies \: \: \: \boxed{ \sf \:v=u+a\times t}$

• Substitute all values :

$: \implies \: \: \sf v=0.1\times 10 \\ \\ \\ : \implies \: \: \sf \: v \: =1\ m/s. \:$

We know that :

$: \implies \: \: \: \boxed{ \sf P = m\times v}$

• Substitute all values :

$\sf : \implies \: \: \: \: \: p =1\times 4 \\ \\ \\\sf : \implies \: \: \: \: \: p =4 \ kg\ m/s$

• Hence The value of velocity and momentum is 1 m/s and 4 kg m/s respectively.