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**Beginner's Kinematics Problem**

## Homework Statement

An x-axis likes along an inclined plane, with the positive x-direction down the plane. Two objects A and B travel along the x-axis.

At t=0, object A starts at x=0 with an initial velocity of 0. At t=1s, object B starts at x=10.00 m with a velocity of -5 m/s. Both objects have an acceleration of positive 2 m/s/s.

At what time and position do the objects collide?

At what time do the objects have the same speed?

## Homework Equations

x

_{f}= x + v

_{i}(t) + 0.5at

^{2}

v

_{f}= v

_{i}+a(t)

## The Attempt at a Solution

a) Equate the two equations (because x final is the same) and solve for t.

OBJECT A: x

_{f}= 0 + (0 m/s)(tf-0 s) + 0.5(2 m/s/s)(tf-0)

^{2}

OBJECT B: x

_{f}= 10 m + (-5 m/s)(tf-1 s) + 0.5(2 m/s/s)(tf-1)

^{2}

I got t= 2.29 seconds using a graphic calculator. Is that correct? Are the equations above correct?

Part b of the question is what's REALLY confusing me. There is no time that I can find that the objects have the same speed.

OBJECT A:

v

_{f}= (0 m/s) + (2.00 m/s/s)(tf-0s)

OBJECT B:

v

_{f}= (-5 m/s/s) + (2.00 m/s/s)(tf-1s)

The two lines, when graphed, never intersect. Also, making object A's equation equal to object B's equation doesn't work either. What am I doing wrong??

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