The velocity of an object with a mass of #2 kg# is given by #v(t)= t^3 + 3 t^2 #. What is the impulse applied to the object at #t= 4 #?

1 Answer
Feb 26, 2016

Answer:

#I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s#
Careful however Impulse is not #mv(t)# evaluate at #t = 4 s#
it is Force applied for a finite amount of time #F*Deltat#
in the limit #I = int_(t_1)^(t_(2))Fdt #

Explanation:

This is a straight implementation of the impulse equation i.e.
#F = m(dv)/dt # Newton law ==> (1)
#I = F dt = m(dv) # Impulse equation ==> (2)
While the question is not clear I will make the assumption the Force was applied for 4 seconds causing the change in speed from
#v(0) = 0 -> v(4)# and #I (4) =2 (4*4^2 +3*4^2) = 7*4^2 = 112 N s#