Question

Racing cars A and B are traveling on circular portions of a race track. At the instant shown, the speed of A is decreasing at the rate of 8 m/s2, and the speed of B is increasing at the rate of 3 m/s2. For the positions shown, determine (a) the velocity of B relative to A, (b) the acceleration of B relative to A.

Answer 1

a)
`V_(B/A) = V_B - V_A`

b)
`a_(B/A) = 11m/s^2`

Step-by-step explanation:

Since we don't have any diagram or image, I will make these assumptions in order to be able to answer the questions:

- They are moving in a straight line

- They both move in the same direction

With these assumptions we can say that their velocities have the same sign, so the velocity of B relative to A would be:

`V_(B/A) = V_B - V_A` If, for example, Vb = 20m/s and Va = 30m/s then:

`V_(B/A) = -10m/s` This would be the answer for part (a)

If they both move in the same direction, their accelerations would be:

`a_A = -8m/s^2` and
`a_B = 3m/s^2` So, the acceleration of B relative to A would be:

`a_(B/A) = a_B - a_A = 3 - (-8) = 11m/s^2`