Question

force of 20 N acts on a body of mass 5kg for 2 seconds initially at rest. findvelocity acquired by body and change in momentum ?​

Answer 1

Given :-

• Force acting on the body is 20N [F=20N]
• Mass of the body is 5 kg [m=5kg]
• The body is  at rest [u =0]
• Time taken = 2 s [t = 2s]

To find :-

• Final velocity (v)
• Change in momentum

Solution :-

We can find the final velocity of the body by using Newtons second law

$\bigstar {\boxed{\sf F = \dfrac{m(v-u)}{t} }}$

Substituting the values ,

$\implies \sf 20 = \dfrac{5(v-0)}{2}$

$\implies \sf 20 = \dfrac{5(v)}{2}$

$\implies \sf 20 \times 2 = 5v$

$\implies \sf 5v = 40$

$\implies \sf v =\dfrac{40}{5}$

$\implies \sf v = 8 m/s$

So, final velocity of the body is 8 m/s

Now calculating the change in momentum .

As we know that ,

$\star{\boxed{\sf Change \: in \: momentum = Final \:momentum - Initial\: momentum }}$

$\implies \sf Final \:momentum = mv$

$\implies \sf Initial \: momentum = mu$

Change in momentum = mv - mu

$\star{\boxed{\sf Change \: in \: momentum = m(v-u) }}$

Substituting the values ,

$\sf\implies \triangle p = 5(8-0)$

$\sf\implies \triangle p = 5(8)$

$\sf\implies \triangle p = 40$

So , change in momentum is 40 kg m/s

Note :-

Δp is denoted as Change in momentum.