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 at an acceleration of 3 m/s2
. The automobile overtakes the
truck after the truck has moved 75 m. Try to draw the figure.
a) How long does it take the auto to overtake the truck?
b) How far was the auto behind the truck initially?
c) What is the velocity of each when they are abreast?
The equations of motion of automobile and truck are given by
"x_a=3t^2\/2=1.5t^2\\\\\nx_t=x_0+2t^2\/2=x_0+t^2"At the instant when automobile overtakes the truck
"x_t=x_a\\\\\nd_t=x_t-x_0=75\\:\\rm m"So
"t^2=75\\\\\n1.5\\times 75=x_0+75\\\\\nx_0=37.5\\\\\nt=\\sqrt{75}=8.7\\:\\rm s"Hence
"x_a=1.5t^2\\\\\nx_t=37.5+t^2""v_a=3t=3\\times 8.7=26\\: {\\rm m\/s}\\\\\nv_t=2t=2\\times 8.7=17\\: {\\rm m\/s}"
Answers:
(a) 8.7\:\rm s
(b) 37.5 m
(c) "v_a=26\\: {\\rm m\/s},\\; v_t=17\\: {\\rm m\/s}"
Comments
Leave a comment