The velocity function is #v(t)=-t^2+4t-3# for a particle moving along a line. Find the displacement of the particle during the time interval [0,5]?

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Answer 1 · 2015-07-26T08:38:45

The problem is illustrated below.

Here, the velocity of the particle is expressed as a function of time as,

#v(t) = - t^2 + 4t - 3#

If #r(t)# is the displacement function, it is given as,

#r(t) = int_(t""_0)^t v(t)*dt#

According to the conditions of the problem, #t""_0 = 0# and #t = 5#.

Thus, the expression becomes,

#r(t) = int_0^5 (-t^2 + 4t - 3)*dt#

#implies r(t) = ( -t^3/3 + 2t^2 -3t)# under the limits #[0,5]#

Thus, #r = -125/3 + 50 - 15#
The units need to be put.