Question #313693

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?

Expert's answer

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}"

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