Question #870b3

2 Answers
Oct 23, 2017

The acceleration is =2(c+6d)ms^-2

Explanation:

The derivative of x^n is

(x^n)'=nx^(n-1)

The displacement is

s(t)=a+bt+ct^2+dt^3

The velocity is the derivative of the displacement

v(t)=s'(t)=b+2ct+3dt^2

The acceleration is the derivative of the velocity

a(t)=v'(t)=a''(t)=2c+6dt

When t=2s

a(2)=2c+6d*2=2c+12d=2(c+6d)ms^-2

Oct 23, 2017

Let's have a look.

Explanation:

Acceleration (a) is the first order derivative of velocity (v), which in turn is first order derivative of displacement (S).

Therefore, acceleration is the second order derivative of displacement.

Now given that rarr

S=dt^3+ct^2+bt+a

:.v=d/dt(S)

:.v=3dt^2+2ct+b

:.a=d/dt(v)=(d^2S)/(dt^2)

:.a=6dt+2c

Now, here acceleration (a) is a function of time (t).

:.a=f(t)

:.a_((t=2))=6dcdot(2)+2c

:.a_((t=2))=12d+2c

:.a_((t=2))=2(c+6d) ms^(-2). (Answer).

Hope it Helps:)