The equation of motion of a particle is s = t3 − 12t, where s is in meters and t is in seconds. (Assume t ≥ 0.) (a) Find the velocity and acceleration as functions of t.

V = 3t² - 12 (velocity as function of t)

a = 6t (acceleration as function of t)

Explanation:

The distance covered by an object is given as a function of time :

s = t³ - 12t

where,

s = distance

t = time

Since, velocity is given as:

V = ds/dt

V = d/dt(t³ - 12t)

Applying derivative:

V = 3t² - 12 (velocity as function of t)

Since, acceleration is given as:

a = dV/dt

a = d/dt(3t² - 12)

Applying derivative:

a = 6t (acceleration as function of t)

electrical potential energy =0.072 j

explanation:

electrical potential energy is given by

u= q δv

q= charge=6 c

δv= potential difference and is given by

δv= e d

e= electric field

d= distance=5 mm=0.005 m

δv=2.4 (0.005)=0.012 v

now electric potential energy= u= q δv

u=6 (0.012)

u=0.072 j