Question

A body of m=1 kg is acled by some force such that its displacement is given bybs=2t²-2t+10 find the work done by all the force in 0 to 2s .

Answer 1

Answer:

64J

Explanation:

The Work-Energy theorem for a variable force states that Kf−Ki=W, where Kf andKi are the final and initial Kinteic energies, with the corresponding velocities vf and vi, and initial and final times of ti=2s and tf=4s.

Given s=t2+2t→v=dsdt=d(t2+2t)dt=2t+2

⇒Kf=12 mv2f=12×2(2×4+2)2=100J

⇒Ki=12 mv2i=12×2(2×2+2)2=36J

⇒W=Kf−Ki=100−36=64J

Answer 2

Answer:

given mass=1kg

displacement = 2t² - 2t + 10

using differentiation,

velocity = 4t - 2

again by differentiation,

acceleration = 4

now, we know

force = mass * acceleration

= 1 * 4

=4

now,

work done = force * displacement

= 4 * (2t²-2t+10)

now,

firstly put

t = 0 then t = 1 and then t= 2

u will get the answers

Explanation:

putting t= 0

u will get, Work Done = 0

putting t = 1

u will get, Work Done = 40J

putting t = 2

u will get, Work Done = 56J