Question

An object is pushed along a rough horizontal surface and released. It slides for 11.0 s before coming to rest and travels a distance of 22.0 cm during the last 1.5 s of its slide. Assuming the acceleration to be uniform throughout

(a) How fast was the object travelling upon release?
(b) How fast was the object travelling when it reached the halfway position in its slide?

Answer 1

(a) 2.15 m/s

(b) 1.52 m/s

Step-by-step explanation:

(a) Given at the end of the slide:

s = 0.220 m

v = 0 m/s

t = 1.5 s

Find: a

s = vt − ½ at²

0.220 = (0) (1.5) − ½ a (1.5)²

a = -0.196 m/s²

Given for the full slide:

v = 0 m/s

a = -0.196 m/s²

t = 11.0 s

Find: u

v = u + at

0 = u + (-0.196) (11)

u = 2.15 m/s

(b) Given for the full slide:

a = -0.196 m/s²

v = 0 m/s

t = 11.0 s

Find: s

s = vt − ½ at²

s = (0) (11.0) − ½ (-0.196) (11.0)²

s = 11.8 m

Given at the midpoint:

s = 11.8/2 = 5.92 m

u = 2.15 m/s

a = -0.196 m/s²

Find: v

v² = u² + 2as

v² = (2.15)² + 2 (-0.196) (5.92)

v = 1.52 m/s