Find the deceleration and Velocity of T³-2T+T

Physics

ScanSolve AI Answer

Step-by-step solution

4 steps
  1. Simplify the given expression for position.

    The position function s(T)s(T) is given by:

    s(T)=T3−2T+Ts(T) = T^3 - 2T + T s(T)=T3−Ts(T) = T^3 - T
  2. Find the velocity function by differentiating the position function with respect to TT.

    Velocity v(T)v(T) is the first derivative of s(T)s(T):

    v(T)=dsdT=ddT(T3−T)v(T) = \frac{ds}{dT} = \frac{d}{dT}(T^3 - T) v(T)=3T2−1v(T) = 3T^2 - 1

    The velocity is 3T2−1\boxed{3T^2 - 1}.

  3. Find the acceleration function by differentiating the velocity function with respect to TT.

    Acceleration a(T)a(T) is the first derivative of v(T)v(T):

    a(T)=dvdT=ddT(3T2−1)a(T) = \frac{dv}{dT} = \frac{d}{dT}(3T^2 - 1) a(T)=6Ta(T) = 6T
  4. Determine the deceleration.

    Deceleration is the negative of acceleration.

    Deceleration=−a(T)\text{Deceleration} = -a(T) Deceleration=−6T\text{Deceleration} = -6T

    The deceleration is −6T\boxed{-6T}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question