Physics help?

Question

A turtle and a hare race. The hare takes off at 4.5 m/s for 15 minutes and the turtle takes off at 0.45 m/s. The hare then slows down to 1.5 m/s for 10 mins. Then it falls asleep for 20 minutes. It wakes up and sprints for the next 15 mins at 6.2 m/s.

a. What is the hare's avg. velocity?
b. What is the total displacement of the hare?
c. What is the turtle's displacement if he continued moving at the same rate for the same amount of time as the hare's total trip?

Answer 1

Hi Jamie,

 

First, you have to change minutes to seconds for each interval.  For first interval, 15 x 60 = 900 seconds.  For second interval, 10 x 60 = 600 seconds.  And final interval, 15 x 60 = 900 seconds.

 

For sleeping minutes, 20 x 60 = 1200 seconds

 

After this conversion, multiply to velocity for each interval (time)  ( x = v t ) and add them up to get total displacement (distance).  If you add them up, you should get 10530 m.

 

v₁       t                             v₂      t₂                             v_f       t_f                f = final phase  or last interval

4.5 x 900 = 4050m       1.5 x 600 = 900m          6.2 x 900 = 5580m

 

If you include sleeping minutes for total time, it will be 60 minutes.  To convert minutes to seconds: 60 min = 3600 seconds.  If you exclude sleeping hours, then it will be 40 minutes or 2400 seconds.

 

So, you got total distance and total time for hare.  It's time to calculate avg velocity.

 

v = x / t  (total time: including sleeping time) (must be in seconds)          

 

v = 10530 m / 3600 s = 2.925 m/s  =  2.9 m/s  (for 2 sig figs)

 

 

For part c, use the total time of hare (60 min = 3600 seconds) to calculate the total displacement (distance) for turtle.

 

v = x / t    -->     x = v  t    x = (0.45) x (3600) = 1620 m (1600 m for 2 sig figs).

 

(sig fig means significant figures)

 

I hope you understood how it got worked out.

 

Good luck to you.

 

Yohan Chu   (LV  NV)

Answer 2

Hare total trip time: 15min+10min+20min+15min = 60min (1hour=3,600sec)

Hare total displacement: 60(4.5x15 +1.5x10+6.2x15)=10530m (10.53km)

Hare average velocity: 10530m/3600 =2,925 m/s

Turtle's displacement: 0.45 * 3600 = 1620 m