An object's two dimensional velocity is given by #v(t) = ( t-2 , 5t^2-3t)#. What is the object's rate and direction of acceleration at #t=2 #?

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Answer 1 · 2016-05-26T15:49:43

#a=17.03" "m/s^2#

#tan alpha=17#

#v(t)=(t-2,5t^2-3t)#

#(d v(t))/(d t)=a(t)#

#a_x(t)=d/(d t) (t-2)=1" "a_x=1" constant"#

#a_y(t)=d/(d t)(5t^2-3t)=10t-3#

#a_y(2)=10*2-3#

#a_y(2)=17#

enter image source here

#a=sqrt(a_x^2+a_y^2)#

#a=sqrt(1^2+17^2)#

#a=17.03" "m/s^2#

#tan alpha=17#