Speed does not rely on the direction of movement so:
#"Average speed" = "Displacement (total distance travelled)"/"Time"#
Displacement (#s#) = Displacement 1 (#s_1#) + Displacement 2 (#s_2#)
#s="speed"xxDeltat#
#s_1=1ms^-1xx8s=8m#
#s_2=7ms^-1xx5s=35m#
#s_("total")=8m+35m=43m#
Time (total) = #8s+5s=13s#
#"Average Speed"=s/t=(43m)/(13s)=3.31ms^-1#
Velocity is reliant on the direction of travel so:
#"Velocity ("v")"=("Final distance from start ("d_"total"")")/("Time ("t")"#
Here we use velocity (#v#) with a direction so that movement North is positive (and movement South is negative)
#Deltad=vxxDeltat#
#d_1=1ms^-1xx8s=8m#
#d_2=-7ms^-1xx5s=-35m#
#d_"total"=d_1+d_2=8m+(-35m)=-27m#
#v=(d_"total")/(t_total) = (-27m)/(13s)=-2.08ms^-1 " North"#
You could also say the velocity is #2.08ms^-1 South#. Since both are equivalent, both are correct, as long as you give the correct direction to go with the answer.
