Question

82. An object of mass 2 kg at rest at origin starts moving
under the action of a force Ể = (3t2 i + 4tį)N
The velocity of the object at t = 2s will be
(1) (3 + 2ſ)m/s (2) (2î + 4ſ) m/s
(3) (4i + 4ſ)m/s (4) (3î - 47)m/s​

Answer 1

Answer:

Option (3) is correct  (4i + 4ſ)m/s

Explanation:

we know that according to newtons second law of motion force is the derivative of momentum with respect to the time.Provided the constant of proportionality is 1.

$F=\frac{dp}{dt}$................(1)

P=mv............................(2)

using (1) and(2) we get,

$F=m\frac{dv}{dt}$

so,$Fdt=mdv$

we have $F=3t^{2}\hat{i}+4t\hat{j}$

m=2 kg

So, $(3t^{2}\hat{i}+4t\hat{j})dt=2dv$

integrate both sides we get

$\int\( (3t^{2}\hat{i}+4t\hat{j})dt=\int\ 2dv$

after integration we get

$\frac{3t^{3} }{3}\hat{i}+\frac{4t^{2} }{2}\hat{j}  = 2v$

$t^{3}\hat{i}+2t^{2}\hat{j} =2v$

so, at t=2 sec

velocity $v=4\hat{i}+4\hat{j}$

Option (3) is correct  (4i + 4ſ)m/s

Answer 2

the answer is option (3)

hope it helps you!