Question

the position x of a particle varies with t as x = at²-bt³. so calculate the acceleration after 2 seconds​

Answer 1

Answer:

here is your answers

Step-by-step explanation:

X = at² - bt³

acceleration means change in velocity per unit time . e.g a = dv/dt .

and we also know, velocity is change in displacement per unit time .e.g v = dx/dt

hence, acceleration = d²x/dt²

now, differentiate x = at² - bt³ with respect to t

dx/dt = 2at - 3bt²

again, differentiate with respect to t

d²x/dt² = 2a - 6bt

according to above we know, d²x/dt² is acceleration so,

acceleration = 2a - 6bt

but question ask acceleration is zero in which time . so,

2a - 6bt = 0

6bt = 2a

t = a/3b