8.
A solid horizontal surface is covered with a thin layer
of oil. A rectangular block of mass m = 0.4 kg is at rest
on this surface. An impulse of 1 Ns is applied to the
block at time t = 0 so that it starts moving along the x-
axis with a velocity v(t) = Voe-t/t, where vo is a
constant and t = 4 s. The displacement of the block at
t = t will be (Take e-1 = 0.37)
(a) 3.7 m () 6.3 m
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4
Answer:
Explanation:
As in the question at t=0 ,body was at rest,but suddenly an impulse was applied on the body on the instant t=0 ,so linear momentum of body increase ,which leads to displacement of body .
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0
v=v
o
e
τ
−t
v
o
=
m
J
=2.5m/s
v=v
o
e
τ
−t
dt
dx
=v
o
e
t
−t
∫
0
x
dx=v
o
∫
0
t
e
τ
−t
dt
∫e
−x
dx=
−1
e
−x
x=v
o
⎣
⎢
⎢
⎢
⎡
τ
1
e
τ
−t
⎦
⎥
⎥
⎥
⎤
0
t
x=2.5(−4)(e
−1
–e
0
)
x=25(−4)(0.37−1)
x=6.30≈6
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