Answered

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Compared to the amount of energy required to accelerate a car from rest to 15 m/s, the amount of energy required to accelerate the same car from 15 m/s to 30 m/s is:
a. the same
b. one quarter as much
c. half as much
d. four times as much
e. one third as much
f. three times as much
g. twice as much

Sagot :

regalmocha17

f. three times as much


Using the formula for kinetic energy:

KE = 1/2(mv^2)

Object 1: rest to 15 m/s

KE = 1/2(15^2)

KE = 112.5 J

Object 2: 15 m/s to 30 m/s

KE = 1/2(30^2)

KE = 450 J

450 J - 112.5 J = 337.5 J

337.5J/112.5 J = 3

Therefore the amount of energy required to accelerated the same car from 15 m/s to 30 m/s is 3 times as much as that required to accelerate the car from rest to 15 m/s.

d. four times as much, the amount of energy required to accelerate the car from 15 m/s to 30 m/s is four times as much as the amount of energy required to accelerate the same car from rest to 15 m/s

Let's evaluate the comparison of the energy required to accelerate the car from rest to 15 m/s to the energy required to accelerate it from 15 m/s to 30 m/s.

The kinetic energy [tex](\(KE\))[/tex] of an object is given by:

[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]

where [tex]\(m\)[/tex] is the mass of the object and [tex]\(v\)[/tex] is its velocity.

For the first scenario (from rest to 15 m/s), the kinetic energy [tex](\(KE_1\))[/tex] is:

[tex]\[ KE_1 = \frac{1}{2} m (15)^2 \][/tex]

For the second scenario (from 15 m/s to 30 m/s), the kinetic energy [tex](\(KE_2\))[/tex] is:

[tex]\[ KE_2 = \frac{1}{2} m (30)^2 \][/tex]

Now, let's compare [tex]\(KE_2\) to \(KE_1\):[/tex]

[tex]\[ \frac{KE_2}{KE_1} = \frac{\frac{1}{2} m (30)^2}{\frac{1}{2} m (15)^2} \][/tex]

[tex]\[ \frac{KE_2}{KE_1} = \frac{900}{225} \][/tex]

[tex]\[ \frac{KE_2}{KE_1} = 4[/tex].

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