An ant is crawling along a yardstick that is pointed with the 0-inch mark to the east and the 36-inch mark to the west. it starts at the 16 inch mark, crawls to the 29-inch mark, then moves to the 14-inch mark. what is the total distance the ant traveled? what was the total displacement of the ant?

Explanation:

Lets put a frame of reference in the problem. Starting the frame of reference at the point with the 0-inch mark, and making the unit vector pointing in the west direction, the ant start at position

Then, moves to

so, the distance traveled here is

after this, the ant travels to

so, the distance traveled here is

The total distance traveled will be:

The displacement is the final position vector minus the initial position vector:

This is 2 inches to the east.

it about 600 mph from what i calculated

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s