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Anika [276]
3 years ago
8

What constant acceleration is required to increase the speed of a car from 30 mi/h to 52 mi/h in 5 seconds? (Round your answer t

o two decimal places.)
Mathematics
1 answer:
Alenkasestr [34]3 years ago
6 0

Answer:

a = 9.84 m/s^2

Step-by-step explanation:

Given:

Initial speed (Vi) = 30 mi/h = 67.1 m/s

Final speed (Vf) = 52 mi/h  = 116.32

Time period(t) = 5 seconds

We know the formula of acceleration in terms of initial speed, final speed and time:

a = \frac{Vf -Vi}{t}

a = \frac{116.32-67.10}{5}

a = 9.84 m/s^2

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A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to
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Answer:

Part 1 : A=250 e^{-0.008223t}

Part 2 : Half life is 84 minutes ( approx )

Step-by-step explanation:

Part 1 : Suppose the function that shows the amount( in grams ) of the substance after t minutes,

A=A_0 e^{kt}

If t = 0 min, A = 250 grams,

250=A_0 e^{0}

\implies A_0 = 250

If t = 250, A = 32 grams,

32 = A_0 e^{250k}

32 = 250 e^{250k}

0.128 = e^{250k}

Taking ln both sides,

\ln(0.128) = 250k

\implies k =\frac{\ln(0.128)}{250}=-0.008223

Hence, the equation that shows this situation,

A=250 e^{-0.008223t}

Part 2 : If A = 250/2 = 125,

125 = 250 e^{-0.008223t}

0.5 = e^{-0.008223t}

Taking ln both sides,

\ln(0.5) = -0.008223t

\implies t =\frac{\ln(0.5)}{-0.008223}\approx 84

Therefore, the half life of the substance would be 84 minutes.

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