Kinematics problem involving velocities

Question

Object A, during the first half of its distance, moved with the velocity of 80 km/h, during the second half: 40 km/h. Object B, during the first half of its time, moved with 80 km/h, during the second half: 40 km/h. Find average velocities of Object A and Object B.

The correct answer: 53.3 km/h and 60 km/h

Answer 1

For object A, set x = total distance and thus each half distance is x/2.

Use v=x/t equation for each half of the distance to solve for t. t=x/v (equation rewritten to solve for t)

t1=(x/2)/80= x/160

t2=(x/2)/40=x/80

t(total)=t1 + t2 = x/160 + x/80 = x/160 + 2x/160 = 3x/160

avg velocity = x(total)/(t(total) = x/(3x/160) = 160x/3x = 160/3 = 53.3 km/h

For object B, set t = total time and set each half of the total time to t/2.

Solve, v=x/t for x (distance) for each half time.

x1= v(t/2) = 80(t/2)= 40t

x2= v(t/2) = 40(t/2)=20t

x(total)= x1+x2= 40t +20t = 60t

avg velocity = x(total)/t(total) =60t/t= 60 km/h