An object travels North at #1 m/s# for #8 s# and then travels South at #7 m/s# for # 5 s#. What are the object's average speed and velocity?

Question

An object travels North at #1  m/s# for #8 s# and then travels South at #7  m/s# for #  5   s#.  What are the object's average speed and velocity?

Benjamin Asiedu · Accepted Answer

Average Speed = #3.31ms^-1#
Average Velocity = #-2.08ms^-1# North (#2.08ms^-1# South)

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.

Nathan Ashcroft · Answer

undefined Average speed = total distance / total time
Average velocity = displacement / total time

Total distance traveled = (1 m/s * 8 s) + (7 m/s * 5 s) = 8m + 35m = 43m
Total time = 8s + 5s = 13s

Average speed = 43m / 13s ≈ 3.31 m/s
Displacement = Final position - Initial position = 0 - 8m = -8m (Southward)
Average velocity = -8m / 13s ≈ -0.62 m/s (Southward)