Question

F(t)
A block of mass 2 kg is free to move along the x-
axis. It is at rest and from t = 0 onwards it is sub-
jected to a time-dependent force F(t) in the x-direc-
tion. The force F(t) varies with
t as shown in the figure. The
ANN
kinetic energy of the block
after 4.5 s is [JEE 2010] o 35
(A) 4.50 J
(B) 7.50 J
(C) 5.06 J
(D) 14.06 J​

Answer 1

option (C) 5.06 J is correct choice

It's tricky question. if you know straight line concept , you can easily get the function of force with respect to time.

ok, don't worry let's try to do it .

graph passing through (0,4N) and (3s,0)

so, slope of graph = (0 - 4)/(3 - 0) = -4/3

and equation of graph of slope -4/3 and passing through (0,4) is given as,

(F - 4) = -4/3(t - 0)

⇒F = 4 - 4/3t

we know, F = ma

so, ma = 4 - 3t

as given m = 2kg

so, 2a = 4 - 4/3t

⇒a = dv/dt = 2 - 2/3t

⇒∫dv = ∫(2 - 2/3t)dt

⇒v - 0 = 2t - 1/3t² [ initially block is in rest ]

putting, t = 4.5 s

so, v = 2(4.5) - 1/3(4.5)² = 2.25 m/s

now kinetic energy of block, K.E = 1/2 mv² = 1/2 × 2 × (2.25)²

= 5.0625 J

hence, option (C) is correct choice.

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