A particle moving with a constant speed traveled rectilinearly from point A of coordinates A(-40.0m, 30.0m) to point B(40.0m, 50.0m) in 4 seconds. It then moves rectilinearly (with another constant speed) from point B to point C (60.0m, 20.0m) in 2 seconds.
a. What is the particle's average speed between points A and C?
b. What is the particle's average acceleration in this trip?

For A to B:

A = -40i + 30j ; B = 40i + 50j

Distance A-B:

(40i + 50j) - (-40i + 30j) = 80i + 20j

Using S = V.t

80i + 20j = V . (4)

Hence, V = (20i + 5j) m/s

For B to C:

B = 40i + 50j ; C = 60i + 20j

Distance B-C:

(60i + 20j) - (40i + 50j) = 20i - 30j

Using S = V.t

20i - 30j = V . (2)

Hence, V = (10i - 15j) m/s

For average velocity:

[(20i + 5j) + (10i - 15j)] / 2

Av. Velocity = (15i - 5j) m/s

For Av. Acceleration, we simply divide the Av. Velocity by the total time required to complete the trip i.e. 4 + 2 sec = 6 sec.

Av. Acc. = (15i - 5j) / 6

Av. Acc. = (2.5i - 0.833j) m/s²