Answer to Question #149059 in Physics for Melanie Belandres

Question

7. An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2 m/s2 and the automobile an acceleration of 3 m/s2. The automobile overtakes the truck after the truck has moved 75 m.
a) How long does it take the automobile to overtake the truck?
b) How far was the car behind the truck initially?
c) What is the velocity of each when they are abreast?

Answer 1

a) $s_=at^2/2\to t=\sqrt{2s/a}=\sqrt{2\cdot75/2}=$ 8.7(s)

b) $s_1=a_1t^2/2\to s_1=3\cdot8.7^2/2=113.5(m)$

$s_0=s_1-s=113.5-75=38.5(m)$

c) $v=at=2\cdot8.7=17.4(m/s)$

$v_1=a_1t=3\cdot8.7=26.1(m/s)$