A graph titled Position versus Time shows time in seconds on the x axis, numbered 0 to 10, Velocity in meters per second on the y axis, numbered 0 to 50. A line labeled A starts at the origin and ends at (4, 40). A line labeled B starts at (4, 40) and ends at (9, 40). A line labeled C starts at (9, 40) and ends at (10, 0). Use the information presented in the graph to answer the questions. Which segments show acceleration? Which segment indicates that the object is slowing down? What is the velocity of segment B? What is the acceleration of segment B?

i)the segment that shows acceleration is segment A.

ii)the segment that shows that the object is slowing down is segment C

iii)the velocity of segment B is 40 meters per second

iv)the acceleration of segment B is zero, 0 meters per second square

Explanation:

Note that coordinates are written as (x,y) so the coordinates given in the question are (time, velocity)

i) acceleration is defined as the increase of velocity with time, segment A moved from origin (0,0) to (4,40) increasing velocity from 0m/s to 40m/s in 4 seconds.

ii) slowing down means that velocity is no longer increasing but decreasing with time. Segment C starts from (4,40) and ends at (10,0) which means the velocity reduces from 40m/s to 10m/s in 6 seconds.

iii) for segment B, (4,40) to (9,40), since the y-axis remains 40 for both cases, the velocity for segment B did not change, it remains 40m/s

iv) acceleration = v-u/t

where v=final velocity and u=initial velocity for segment B, t= time taken for change in velocity

(4,40) to (9,40)

acceleration = 40-40 / 9-4 = 0/5 = 0 meters per second square

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west