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EXERCISE 2.6 A particle follows a planar path defined by x = kč, y = 2k[1 − exp()], such that its speed is v=B², where k and ß are constants. Determine the velocity and acceleration at = 0.5.

EXERCISE 2.6 A particle follows a planar path defined by x = kč, y = 2k[1 − exp()], such that its speed is v=B², where k and ß are constants. Determine the velocity and acceleration at = 0.5.

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EXERCISE 2.6 A particle follows a planar path defined by x = kč, y = 2k[1 − exp(š)], such that its speed is v = Bč, where k and ß are constants. Determine the velocity and acceleration at = 0.5.
Transcribed Image Text:EXERCISE 2.6 A particle follows a planar path defined by x = kč, y = 2k[1 − exp(š)], such that its speed is v = Bč, where k and ß are constants. Determine the velocity and acceleration at = 0.5.
Expert Solution
Step 1

We have given 

x=kξ   and    y= 2k [ 1 - eξ ]

position vector is given by 

(r) → = xi +yj  

     =( kξ )i + 2k [ 1 - eξ ] j

now velocity  V(ξ)→=dr¯dξ=ddξ{( kξ )i + 2k [ 1 - eξ ] j}

V→(ξ)=ki - 2keξ j

V→(ξ)=k( i -2e0.5 j) 

V(ξ)=k2+(-2keξ)2

V(0.5)=k2+(-2ke0.5)2

V(0.5)=k 1+4e ..............(1)

 

 

 

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