Answer to Question #149701 in Calculus for Maow

Question

An automobiles velocity starting from rest is where v is measured in feet per second. Find
i) Its velocity after 5 seconds
ii) Its average velocity during the 10th second
iii) Its acceleration after 2 seconds
iv) Its average acceleration from t=2 to t=4

Answer 1

i)Velocity after 5 sec is: V=V₀+at,

V₀=0, V=5a

ii) Average velocity V_avr= S_total/t_total

S=at²/2. In our case t=10 : V_avr=at²/(2×10), V_avr=5a

iii)acceleration after 2 sec, we can derive it from the formual:V=V₀+at, from here we find a, a=V/t, a=V/2.

iv) average acceleration from t=2 to t=4 can be found by (a₂+a₄)/2.

a₂=V₂/2, a₄₌V₄/4. So

a_avr=(V₂/2+V₄/4)/2,

a_avr=(2V₂+V₄)/8