# Circular Motion of two bikes

1. Jan 24, 2004

### jjiimmyy101

Two cyclists A and B, are traveling counterclockwise around a circular track at a constant speed of 8 ft/sec at the instant shown. If the speed of A is increased at aA = SA ft/sec^2, where SA is in ft, determine the distance measured counterclockwise along the track from B to A between the cyclists when time is = 1 sec. What is the magnitude of the acceleration of each cyclist at the instant?

To find the length of an arc, you use the equation arc=theta*radius, but how do you encorporate the time into this? I don't know how far cyclist A moves.

To find the magnitude of acceleration you can use the sqrt of a(normal)^2 + a(tangential)^2.

aB =1.28 ft/sec^2

because a(tangential)=0 (constant velocity) and a(normal)=64/50

I don't know what aA is equal to.

Any suggestions?

I posted a picture too.

#### Attached Files:

• ###### circ.gif
File size:
2.9 KB
Views:
105
Last edited: Jan 24, 2004
2. Jan 25, 2004

### Staff: Mentor

First find the distance between A & B at time t=0 (the instant shown). Then find out how far each moves in the next second. If it wasn't for that fact that A is accelerating, they would move the same distance, thus maintaining the same separation. But A gains some distance over B: &Delta;X = 1/2at2.

Also, A gains some speed: &Delta;V = at.

3. Jan 25, 2004

### jjiimmyy101

at time t=0 the distance between them is 104.72ft

B moves 8ft in the next second because it is constant

but i still don't get how far A moves.

and how do I use deltaX and deltaV

Last edited: Jan 25, 2004
4. Jan 25, 2004

### Staff: Mentor

You need to understand the basic formulas for uniform accelerated motion. One key relation is $d = v_0t + \frac{1}{2}at^2$, which describes the distance traveled in time t. ($v_0$ is the initial speed.) Another useful formula gives the speed after time t: $v = v_0 + at$. You will need both of these to understand how "A" moves.

B is just moving at a constant speed (tangential acceleration = 0). I believe you understand that, but note that the above equations apply if you set a=0. (Please try this!)

Of course, the above only applies to the tangential motion. To find the full acceleration, you must add the centripetal acceleration.

Note: &Delta; just means "change"; &Delta;X means change in x.

5. Jan 25, 2004

Thanks!