The position of a particle moving along the x axis is given in cm by #x=9.47 + 1.85t^3#, where #t# is in seconds. What is the average velocity during #t = 2 sec to t=3 sec#? What is the instantaneous velocity at #t = 2.5 sec?

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Answer 1 · 2017-09-25T12:18:27

The average velocity is #=0.3515ms^-1#
The instantaneous velocity is #=0.346775ms^-1#

The position of the particle is

#x(t)=0.01(9.47+1.85t^3)m#

The velocity is the derivative of the position

#v(t)=x'(t)=0.01*3*1.85t^2=0.0555t^2#

The instantaneous velocity at #t=2.5s# is

#v(2.5)=0.0555*2.5^2=0.346875ms^-1#

The average velocity is

#(3-2)barv=int_2^3 0.0555t^2dt=0.0555[t^3/3]_2^3#

#barv=0.0555(9-8/3)=0.0555*19/3=0.3515ms^-1#