Position coordinate of a particle confined to

move along a straight line is given by s=

2t

3-24t + 6, where s is measured in meters

from a convenient origin and t is in seconds.

Determine: (a) time required for the particle

to reach a velocity of 72 m/s from its initial

condition at t = 0, (b) acceleration of the

particle when v = 30 m/s, and (c) net

displacement of the particle during the

interval from t = 1 s to t = 4 s.

Question

Physics

Everett

10 February, 00:07

Position coordinate of a particle confined to

move along a straight line is given by s=

2t

3-24t + 6, where s is measured in meters

from a convenient origin and t is in seconds.

Determine: (a) time required for the particle

to reach a velocity of 72 m/s from its initial

condition at t = 0, (b) acceleration of the

particle when v = 30 m/s, and (c) net

displacement of the particle during the

interval from t = 1 s to t = 4 s.

+4

Answers (1)

Know the Answer?

Craig Hernandez · Answer 1

a) 4 s

b) 36 m/s²

c) 54 m

Explanation:

s = 2t³ - 24t + 6

a) Find t when v = 72 m/s.

v = ds/dt

v = 6t² - 24

72 = 6t² - 24

6t² = 96

t = 4

b) Find a when v = 30 m/s.

a = dv/dt

a = 12t

When v = 30:

30 = 6t² - 24

6t² = 54

t = 3

a = 36

c) Find Δs between t = 1 and t = 4

Δs = (2 (4) ³ - 24 (4) + 6) - (2 (1) ³ - 24 (1) + 6)

Δs = 38 - (-16)

Δs = 54