Question

The momentum of a body is given by
P=(10t²î. + 5t j cap)Kgm/s
Find the force acting on the body at t=2s.

Answer 1

dp/dt=F

20t+5=F

45=F

so at t=2 sec

force is equal to 45N

Answer 2

The force acting on the body at t = 2 s is 40.31 N.

Explanation:

Given that,

Momentum of a body, $P=(10t^2i+5tj)\ kg-m/s$

To find,

The force acting on the body at t = 2 s

Solution,

The rate of change of linear momentum of a body is directly proportional to the external force acting on it such that,

$F=\dfrac{dP}{dt}$

$F=\dfrac{d(10t^2i+5tj)}{dt}$

$F=(20t\ i+5\ j)\ N$

At t = 2 s,

$F=20\times 2+5\ j$

$F=(40\ i+5\ j)\ N$

$|F|=\sqrt{40^2+5^2} =40.31\ N$

So, the force acting on the body at t = 2 s is 40.31 N.

Learn more,

Second law of motion

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