Question

18. The position of a particle moving along the x-axis is given by x-30t-30t, where x is achieves its maximum speed in the positive x-direction? A) 42 m B) 9.8 m C) 3 m D) 27 m E) 5.6 m

Answer 1

given

x = 30t² - 30 t⁴

we know that

v = dx/dt = d(30t² - 30 t⁴)/dt

v = 60 t - 120 t³

for maximum velocity dv/dt = 0

d(60 t - 120 t³)/dt = 0

60 - 360 t² = 0

t² = 60/360 = 1/6

t = 1/ sec

so this instant X = ?

put t = 1/ in x

x =  30t² - 30 t⁴

= 30 (1/)² - 30(1/)⁴

x = 4.2 m

answer