micha ran 2 miles north in 20 minutes. she then turned back and ran 1 mile in 15 minutes. to cool down, she walked the rest of the way home. it took her 20 minutes.

what was micha's average velocity for her run north?

what was micha's average velocity for the whole trip?

what was her average speed for her entire jog?

Explanation:

Given data,

The distance Micha run towards the north, d₁ = 2 miles

The time taken by Micha to run 2 miles is, t₁ = 20 min

                                                                     = 0.33 h

The displacement towards the south, d₂ = -1 mile

The running duration, t₂ = 15 min

                                        = 0.25 h

Walked displacement, d₃ = -1 mile

The time period to cover that distance, t₃ = 0.33 h

1) The average velocity towards north,

                                  v₁ = d₁ / t₁

                                      = 2 / 0.33

                                      = 6.06 miles/hr

Hence, Micha's average velocity for her run north, v₁ = 6.06 miles/hr

2) The average velocity for whole trip,

                         V = (v₁ + v₂ + v₃) / 3

     The velocity towards south,

                         v₂ = d₂ / t₂

                              = -1 / 0.25 h

                              = -4 miles / hr

  The walked velocity,

                           v₃ = d₃ / t₃

                               = -1 / 0.33

                               = - 3.03 miles/hr

∴ The average velocity,

                        V = (v₁ + v₂ + v₃) / 3

                             = (6.06 - 4 -3.03)/3

                             = - 0.32 miles/hr

Hence, Micha's average velocity for the whole trip, V = - 0.32 miles/hr

3) The average speed for her entire jog,

      The velocity of her jog, v₃ = - 3.03 miles/hr

∴ Speed,

                     s = |v|

                        = 3.03 miles / hr

Hence, the speed of her jog is, s = 3.03 miles / hr