Two cars are driving toward each other along a straight road. Their seperation distance is l-(r1+r2)t, where l is their original seperation distance and r, and r2 are their speeds. will the cars meet? When? what if they are goingin the same direction and not driving toward one another? will they meet then?

1) yes, at time of

2) only if the car behind is faster; at time

Step-by-step explanation:

1)

The separation distance between the two cars is given by

where

I is the original separation

is the speed of the 1st car

is the speed of the 2nd car

The positive sign between the speeds of the two cars tells us that the two cars are going into opposite directions (so, the relative velocity of the two cars is the sum of the two velocities).

In order for the two cars to meet, this separation distance must go to zero:

Therefore, this will happen at a time t of:

2)

If the two cars were going in the same direction, then the relative velocity of the two cars would be (assuming car 1 is behind car 2)

So the separation distance between the two cars would be

Therefore, the two cars would meet at a time t of

However, we must notice that there is a condition for this to occur: in fact, the time can only be positive, so it must be

Which means ,the car behind must go faster than the car ahead, otherwise the two cars will never meet.

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.