Question

time is of a particle is given by x^2 +x (x>0)
find its retardation

Answer 1

retardation = negative of acceleration?

Answer 2

ya

Answer 3

so if s(x) = x^2 + x
then velocity v(t) = ds/dt and acceleration a(t) = d^2s/dt^2

So find the second derivative.

Answer 4

Wait. The position of a particle at time t is s(t) = t^2 + t. Or is the question saying something else?

Answer 5

time

Answer 6

So you're saying that x is the particle's displacement at it satisfies the relation that at time t:
t = x^2 + x ?

Answer 7

yes

Answer 8

Ok. In that case, solve this equation for x and then differentiate it.

So you tell me: what is x as a function of t?

Answer 9

quadratic roots?

Answer 10

x^2 + x - t = 0. Solve for x

Answer 11

Found the expression for x yet?

Answer 12

Quadratic formula. a = 1, b = 1, c = -t