Compute the displacement of the particle, Mechanical Engineering

Compute the displacement of the particle:

The acceleration time diagram for particle is as specified below .Computed velocity of the particle at several time intervals, plot velocity time diagram and computed the displacement of the particle at several intervals. Suppose initial velocity v0 = 0 and initial displacement s0 = 5.30 cm.

Solution

We have

dv/ dt  = a,   or          dv = a dt

929_Compute the displacement of the particle.png

∴ v1  - v0  = Area of (a - t ) diagram between t = 0 and t =1 seconds

∴ v1  = v0  + 10 × 1                 v0  = 0

= 10 cm / sec

Likewise,

∴ v2  - v0  = Area of (a - t ) diagram between t = 0 and t = 2 seconds

= v0  + 10 × 2

= 20 cm / sec

And         v3  = 30 cm / sec

We have ds/ dt  = v, or ds = v dt

202_Compute the displacement of the particle1.png

or s1  - s0  = Area of (v - t ) diagram among t = 0 and t =1 seconds

∴ s1 = s0 + (½) × 1 × 10

= 5.30 + 5.0

= 10.30 cm .

s2  - s0  = Area of (v - t ) diagram among t = 0 and t = 2 seconds

         = 5.3 + (½) × 20 × 2

= 25.3 cm .

s3  - s0  = Area of (v - t ) diagram among t = 0 and t = 3 seconds

s3  = 5.3 + (½) × 30 × 3 = 50.3 cm .

Posted Date: 1/29/2013 1:41:12 AM | Location : United States







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