The-position-of-a-body-at-time-t-in-seconds-is-given-by-s-t-3-4-what-is-the-velocity-and-acceleration-of-the-object-at-time-t-5-Mastermind-

Question Number 170411 by Mastermind last updated on 23/May/22

T h e p o s i t i o n o f a b o d y a t t i m e t (i n

s e c o n d s) i s g i v e n b y s = t^{3} - 4, w h a t i s

t h e v e l o c i t y a n d a c c e l e r a t i o n o f t h e

o b j e c t a t t i m e t = 5 ?

M a s t e r m i n d

Answered by alephzero last updated on 23/May/22

velocity = \frac{d s}{d t}

acceleration = \frac{d^{2} s}{{d t}^{2}}

\frac{d s}{d t} = \frac{d (t^{3} - 4)}{d t} = \frac{d (t^{3})}{d t} - \frac{d (4)}{d t} =

= 3 t^{2} - 0 = 3 t^{2}

\frac{d^{2} s}{{d t}^{2}} = \frac{d (\frac{d s}{d t})}{d t} = \frac{d (3 t^{2})}{d t} = 3 \frac{d (t^{2})}{d t} = 3 \times 2 t

= 6 t

velocity at time 5 = \frac{d s}{d t} ∣_{5} = 3 {(5)}^{2} =

= 3 \times 25 = 75

acceleration at time 5 = \frac{d^{2} s}{{d t}^{2}} ∣_{5} = 6 \times 5

= 30

Commented by Mastermind last updated on 24/May/22

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