# Velocity and aceleration relative

Hello Everybody...

i have some problems to start with this problem someone can help me?
thanks

in the figure, block A moves to the left with a speed of 1m / s, decreasing at a rate of 0.5 m/s2 and block C is fixed. determine the velocity of B relative to A and the acceleration of B relative to A

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Consider this.

Imagine the distance between the pulley and Block C is 1 meter. The distance of the rope is 2 meters since it travels "down and back" from Block C.

So, now lets move the pulley 2 meters away from Block C. Now the rope travels down 2 meters to the pulley and back 2 meters from Block C. This is a total of 4 meters of rope.

So, now lets move the pulley 3 meters away from Block C. Now the rope travels down 3 meters to the pulley and back 3 meters from Block C. This is a total of 6 meters of rope.

This pattern shows that

for whatever distance the pulley moves, its passes though twice as much rope.

Therefore, since the pulley is connected to Block A and the end of the rope is connected to Block B, we can say that Block B moves twice as fast as Block A.