08.12.2021

A particle travels along a straight line from a point A on the line. Its velocity after t seconds is (48-3t)cm/s. If its distance from A after t seconds is s cm, find s in terms of t. Hence find the time that elapses before the particle is back again at A.

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09.07.2023, solved by verified expert
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A particle travels along a straight line from, №18010910, 08.12.2021 14:42

16 s

Step-by-step explanation:

Given:

s = su = 0v = 48 - 3ta = t = t

Substituting values into SUVAT formula to find s in terms of t:

      A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

To find the time that elapses before the particle is back at A, set s to zero and solve for t:

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

A particle travels along a straight line from, №18010910, 08.12.2021 14:42

Therefore, t = 0 and t = 16, so the time that elapses before the particle is back again at A is 16 s

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Mathematics
Step-by-step answer
P Answered by Specialist

\sf s=\left(24t-\dfrac32t^2\right) \ cm

16 s

Step-by-step explanation:

Given:

s = su = 0v = 48 - 3ta = t = t

Substituting values into SUVAT formula to find s in terms of t:

      \sf s=\dfrac12(u+v)t

\implies \sf s=\dfrac12(0+48-3t)t

\implies \sf s=\dfrac12(48-3t)t

\implies \sf s=24t-\dfrac32t^2

To find the time that elapses before the particle is back at A, set s to zero and solve for t:

\sf \implies 24t-\dfrac32t^2=0

\sf \implies t(24-\dfrac32t)=0

\sf So \  t=0 \ and \ 24-\dfrac32t=0

\sf \implies 24-\dfrac32t=0

\sf \implies \dfrac32t=24

\sf \implies t=16

Therefore, t = 0 and t = 16, so the time that elapses before the particle is back again at A is 16 s

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The solution is given in the image below

The solution is given in the image below

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