Nathan accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 s.

a. What is Nathanâs acceleration?

b. What is Nathanâs displacement during this time interval?

c. What is Nathanâs average velocity during this time interval?

a) Nathan's acceleration is 5 m/s² b) Nathan's displacement during this time interval is 15.625 mc) Nathan's average velocity during this time interval is 6.25 m/s

Explanation:

a) We have equation of motion v = u + at

Initial velocity, u = 0 m/s

Final velocity, v = 12.5 m/s

Time, t = 2.5 s

Substituting

v = u + at

1.25 = 0 + a x 2.5

a = 5 m/s²

Nathan's acceleration is 5 m/s²

b) We have equation of motion s = ut + 0.5 at²

Initial velocity, u = 0 m/s

Acceleration, a = 5 m/s²

Time, t = 2.5 s

Substituting

s = ut + 0.5 at²

s = 0 x 2.5 + 0.5 x 5 x 2.5²

s = 15.625 m

Nathan's displacement during this time interval is 15.625 m

c) Displacement = 15.625 m

Time = 2.5 s

We have

Displacement = Time x Average velocity

15.625 = 2.5 x Average velocity

Average velocity = 6.25 m/s

Nathan's average velocity during this time interval is 6.25 m/s