Question

If x denotes displacement in time t and x=acost then acceleration is

Answer 1

your question is ----> If x denotes displacement in time t and x=a cos$\omega$t for $\omega$ =1 then acceleration will be?

solution : if x denotes displacement on time and x varies as x = acos$\imega$t ......(1)

we know, velocity is the rate of change of displacement with respect to time.

i.e., dx/dt = v

and acceleration is the rate of change of velocity with respect to time,

i.e., dv/dt = A

so, for finding acceleration we have to differentiate the displacement function twice with respect to time.

now, differentiating x with respect to time.

dx/dt = v = a . d(cos$\imega$t)/dt = -a$\imega$sin$\imega$t

hence, v = -a$\imega$sin$\imega$t

again, differentiating v with respect to time,

dv/dt = A = -a$\imega$ d(sin$\imega$t)/dt = -a$\imega$cos$\imega$t

now putting, $\imega$ = 1

hence, acceleration, A = -acost