Variable acceleration?

The velocity v ms-1 of a particle after t seconds is given by v=t−3t2
The initial displacement of the particle from the origin is 3m.

The displacement of the particle from the origin after 5 seconds is ____m

2 Answers
Douglas K.
Apr 19, 2018

#x = -219/2" m"#

Explanation:

We know that #v = dx/dt#:

#dx/dt = t-3t^2#

where #x# is the displacement

Integrating:

#x = int t -3t^2 dt#

#x = t^2/2-t^2+x_0#

We are told that #x_0 = 3" m"#

#x = t^2/2-t^3+3" m"#

Evaluate at #t = 5" s"#

#x = 5^2/2-5^3+3" m"#

#x = -219/2" m"#

Shiva Prakash M V
Apr 19, 2018

the displacement of the particle after 5 seconds is
#s=-109.5#

Explanation:

#v=t-3t^2#
#v=(ds)/(dt)#

#(ds)/(dt)=t-3t^2#

#ds=(t-3t^2)dt#
#intds=int(t-3t^2)dt#

#s=s_0+1/2t^2-t^3#

#s=3,t=0#

#3=s_0+1/2(0)^2-(0)^3#

#s_0=3#

#s=3+1/2t^2-t^3#

Substitute t=5sec

#s=3+1/2(5)^2-(5)^3#

#s=3+25/2-125#

#s=3+12.5-125#

#s=15.5-125#

#s=-109.5#
Hence, the displacement of the particle after 5 seconds is
#s=-109.5#

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