The graph below shows the variation of a force (F) with time (t) on a body which is moving in a straight line. Dependence of force on time is F \propto t^n . Initially body is at rest If the speed of the object is 2 m/s at 3 s, the speed at 4 s will be approximately (in m/s)

KVPY SX SB Exam 2018 Question Paper

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The graph below shows the variation of a force (F) with time (t) on a body which is moving in a straight line.
Dependence of force on time is

F ∝ t^n

. Initially body is at rest

If the speed of the object is 2 m/s at 3 s, the speed at 4 s will be approximately (in m/s)

Solution:

Suppose

F = Kt^n

from graph

2=K2^n

16 = K4^n = K(2^{2n})

2^n = 8

n = 3
&

K=1/4

F={mdv}/{dt}

{∆V}=1/m∫Fdt

{∆V}_1=K/m∫↖{3}↙{0}t ^3dt =2

{∆V}_2=K/m∫↖{4}↙{0}t ^3dt

{∆V}_2={2∫↖{4}↙{0}t ^3dt}/{∫↖{3}↙{0}t ^3dt}=6.5m \/ s

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