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Question

The velocity function is
#v(t)=t^2−4t+3# for a particle moving along a line. Find the displacement (net distance covered) of the particle during the time interval #[−1,6]#.

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Answer 1 · 2017-12-02T07:56:08

#14mcolor(white)(x)("or any other unit length")#

The function can be represented on a graph:
graph{x^2-4x+3 [-1, 6, -5, 5]}}

The area under the graph will give you your displacement, since #s=v*t# #(m=ms^(-1)*s)#

The area between two points is found by integration, wi the respective bounds.

#s=int_(-1)^6t^2-4t+3dt#
#=[2t-4]_(-1)^6#
#=[2(6)-4]-[2(-1)-4]#
#=8-(-6)#
#=8+6#
#=14m#