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

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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