An automobile and a truck start from rest at the same instant, with the automobi

Question

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 2.80 m/s2, and the automobile an acceleration of 3.60 m/s2. The automobile overtakes the truck after the truck has moved 59.5 m. (a) How much time does it take the automobile to overtake the truck? s (b) How far was the automobile behind the truck initially? m (c) What is the speed of each when they are abreast? automobile: m/s truckL m/s (d) On a single graph, sketch the position of each vehicle as a function of time. Take x = 0 at the initial location of the truck. (Do this on paper. Your instructor may ask you to turn in this graph.)

Explanation / Answer

Use the formula:s=1/2at2;//since initial speed is 0.

suppose automible is y distance behind the truck initially.so the equation will become

x+y=1/2*3.6*t2;................e.q.(1)//from given data

x=1/2*2.8*t2;..........e.q(2)//from given data where x is the distance covered by truck.

we have x=59.5 m;

from equation 2

59.5=1/2*2.8*t2;

t=6.519 sec; ans (a)

using equation 1 and 2 we will get

y=0.4*t2;

by putting value of t2 we will have

y=0.4*595/14;

y=17 meters; ans(b)

now use formula v2=u2+2as;

since u=0;

v2=2as;

so speed of truck:2*2.8*59.5=18.2538 m/s;

speed of automobile=2*3.6*(59.5+17)=23.4691 m/s. ans(c)

ans(d): use s=ut+1/2at2 to plot the graph for time and distance.

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