Question

5 A body of mass 1 kg is acted on by a force () which varies with time (t) as shown in the graph below. The momentum acquired by the body in 2 s if it starts from rest is
(1) 2.5 NS
(2) 10 NS
(4) 5 Ns
(3) 1 NS ​

Answer 1

Answer:

5Ns

please mark as brainliest

Answer 2

Given :

Mass of the body = 1 kg

Maximum force acts on the body = 5 N

Time interval = 2 s

To Find :

The momentum acquired by the body in 2 s.

Concept :

As per Newton's second law of motion, force is defined as the rate of change of momentum per unit time.

Mathematically,

$:\implies\:\underline{\boxed{\bf{\purple{F=\dfrac{\Delta p}{\Delta t}}}}}$

• F denotes force
• ∆p denotes change in momentum
• ∆t denotes time interval

As per formula we can say that,

The area under F - t will give magnitude of ∆p.

By substituting the given values;

$\sf\implies\:\Delta p = Area\:of\:F- t\:graph$

$\sf\implies\:\Delta p=\dfrac{1}{2}\times Base\times Perpendicular$

$\sf\implies\:\Delta p=\dfrac{1}{2}\times (2-0)\times(5-0)$

$\sf\implies\:\Delta p=\dfrac{10}{2}$

$\implies\:\underline{\boxed{\bf{\gray{\Delta p =5\:Ns}}}}$