Question

Question (29)
The displacement of a body of mass 2 kg as a function of time is given by x = 2t2 + 5 where x is in metre and 't'in
seconds. The increase in its kinetic energy one second after the body starts to move isद डिस्प्लेसमेंट ऑफ द बॉडी ऑफ मास 2 केजी एंड फंक्शन ऑफ टाइम इज गिवन बाय एक्स इक्वल टू 20 स्क्वायर प्लस 5 वेयर एक्सिस इन मीटर आईटी इन सेकंड द इनक्रीस इन इट्स काइनेटिक एनर्जी ऑब्टेंड आफ्टर द बॉडी स्टार्स टू मूवीस ​

Answer 1

Answer:

increase in KE = 16 J

Step-by-step explanation:

$\boxed{Given,}$

The displacement of a body of mass 2 kg as a function of time is given by

x = 2t² + 5

$\boxed{To \ find,}$

The increase in its kinetic energy one second after the body starts to move is

$\boxed{Solution,}$

let's find the velocity first..

we get velocity by differentiation of displacement

$v=\frac{dx}{dt} \\\\ v=\frac{d}{dt} (2t^2+5) \\\\ v=\frac{d}{dt} (2t^2)+\frac{d}{dt}(5) \\\\ v=4t+0\\\\v=4t \\\\ v=4(1) \\\\ v=4 \ m/s$

$Kinetic \ energy \ after \ one \ second=\frac{1}{2} mv^2$

                                                      = $\frac{1}{2} \times 2 \times (4)^2$

                                                      = 4²

                                                      = 16 J

Initial Kinetic Energy = 0 [body at rest]

Increase in Kinetic Energy = 16 - 0

                                            = 16 J

The increase in its kinetic energy one second after the body starts to move is 16 J.