Based on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Know that b = 0.80 m and that v = 1 m/s when x = 0. Determine the velocity of the particle when x = –1 m.

Question
Asked Sep 20, 2019

Based on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Know that b = 0.80 m and that v = 1 m/s when x = 0.

 

Determine the velocity of the particle when x = –1 m.

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Expert Answer

Step 1

The acceleration of the particle is given by the equation:

Where (a) in m/s2 and (x) is in meters.

Also the given condition is that: v =1m/s when x= 0 and b = 0.8 m.

0.1+sin
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0.1+sin

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Step 2

The basic kinematics relation is given by the equation, if a = a(x)  then,

 

dv
-a(x)
dv
V
0.1+sin
0.8
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dv -a(x) dv V 0.1+sin 0.8

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Step 3

Now, integrate the equation within t...

0.1+sin
|dx
'0.8
0.1x-0.8cos
0.8
x
[ -1]=-
lx-0)-08| соз.
COs
0.8
0.8
1
1
--0.lx +0.8cos-
2
0.8x1
0.8
2
х
-0.8+0.5
0.8
v20.10.8cos-
2
х
0.3
0.8
- -0.1x +0.8cos
2
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0.1+sin |dx '0.8 0.1x-0.8cos 0.8 x [ -1]=- lx-0)-08| соз. COs 0.8 0.8 1 1 --0.lx +0.8cos- 2 0.8x1 0.8 2 х -0.8+0.5 0.8 v20.10.8cos- 2 х 0.3 0.8 - -0.1x +0.8cos 2

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