Question

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.​

Answer 1

Answer:

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