A car and a truck are heading directly toward one another on a straight and narr

Question

A car and a truck are heading directly toward one another on a straight and narrow street, but they avoid a head-on collision by simultaneously applying their brakes at t=0. The resulting velocity-versus-time graphs are shown in the figure

What is the separation between the car and the truck when they have come to rest, given that at t=0 the car is at x = 16 m and the truck is at x = -53 m ? (Note that this information determines which line in the graph corresponds to which vehicle.)

Explanation / Answer

Soolution-

From the graph we can notice that both vehicles retarded uniformly to zero velocity.

The distance traversed can be find out by finding the area under each v-t graph . So total area is the total distance traversed after the application brakes at t=0.

Therefore , Total distance=(0.5*10*2.5+0.5*15*3.5)

=38.75 m

The distance between the vechile at 0

=16-(-53)

=69 m

So distance of seperation between the vechile when the two vehicles will come to rest will be

=>69- 38.75

= 30.25 m

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