A horse trots at 10m/s for 5 s and then turns around and walks back in the other direction at 2.5m/s for 30 s.

a) what distance did the horse travel?
b) what is its displacement?
c) what is its average speed?
d) what is its average velocity?

forward = 50 m

then back = -75 m
a) 50 + 75
b) 50 - 75
c ) a/35
d) b/35

d = 10*5 + 2.5*30 = 50 + 75.

b. Disp. = 50 - 75 = -25 m. or 25 m below starting point.

c. r * t = 50 + 75.
r = (50 + 75)/t = (50 + 75)/35 = a/35.

d. V * t = (50 - 75)/35 = b/35.
.

To calculate the answers to these questions, we need to use the formulas for distance, displacement, average speed, and average velocity. Let's go through each question step by step.

a) To find the distance the horse traveled, we can calculate the sum of the distances for each leg of the journey. The horse trotted at 10 m/s for 5 seconds, covering a distance of:

Distance of trotting = Speed × Time = 10 m/s × 5 s = 50 meters.

Then, the horse turned around and walked at 2.5 m/s for 30 seconds, traveling a distance of:

Distance of walking = Speed × Time = 2.5 m/s × 30 s = 75 meters.

The total distance traveled is the sum of these two distances:

Total distance traveled = Distance of trotting + Distance of walking = 50 m + 75 m = 125 meters.

So, the horse traveled a distance of 125 meters.

b) Displacement is the straight-line distance and direction between the starting point and ending point. In this case, since the horse returns to the starting point, the displacement is zero. So, the displacement of the horse is 0 meters.

c) Average speed is the total distance traveled divided by the total time taken:

Average speed = Total Distance / Total Time.

We've already calculated that the total distance traveled is 125 meters. The total time taken is the sum of the time taken for trotting (5 seconds) and walking (30 seconds):

Total Time = Time of trotting + Time of walking = 5 s + 30 s= 35 seconds.

Therefore, the average speed of the horse is:

Average speed = 125 m / 35 s = 3.57 m/s (rounded to two decimal places).

So, the average speed of the horse is approximately 3.57 m/s.

d) Average velocity is the displacement divided by the total time taken:

Average velocity = Displacement / Total Time.

The displacement in this case is 0 meters, as the horse returns to its starting point. We've already calculated that the total time taken is 35 seconds, so:

Average velocity = 0 m / 35 s = 0 m/s.

Therefore, the average velocity of the horse is 0 m/s.

In summary:
a) The horse traveled a distance of 125 meters.
b) The horse had a displacement of 0 meters.
c) The horse had an average speed of approximately 3.57 m/s.
d) The horse had an average velocity of 0 m/s.