## Plug variables expressed in SI units in the kinematic equation given in article: a = -v0^2/(2sg). What value of g you get as expressed in g’

Question

Plug variables expressed in SI units in the kinematic equation given in article: a = -v0^2/(2sg). What value of g you get as expressed in g’s where g = 9.8 m/s^2 1 point the same as in English units smaller larger this calculation cannot be performed in SI units If the initial velocity of player is doubled then the absolute acceleration would * 1 point decrease 2x stays the same increase 2x increase 4x If stopping distance is decreased 2x then the acceleration would * 1 point decrease 2x stay the same increase 2x increase 4x Other: Hockey player having initial velocity 20 m/s and helmet having padding 5 cm hits head on his twin brother. The acceleration of his brain is most closely equal to * 1 point 0.4g 4g 40g 400g

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1 week 2021-07-22T21:47:34+00:00 1 Answers 1 views 0

1) acceleration is increased by a factor of four 4X

2) the acceleration increases a factor of 2X

3) the correct answer of 400g

Explanation:

This is a kinematics exercise, where you use the velocity equation to obtain the acceleration, with the final velocity equal to zero.

v² = v₀² + 2 a x

0 = v₀² + 2 a x

a = – v₀² / 2 x

In the case of wanting to give the acceleration as a function of g, we can find the relationship between the two quantities

a / g = – v₀² / (2 x g)

1. The initial velocity is doubled, how much the acceleration is worth

a/g = – (2v₀) 2 / 2xg

a = 4 (-v₀² / 2xg) g

acceleration is increased by a factor of four 4X

2. if the stopping distance is reduced by 2, that is, x = x₀ / 2

we substitute

a/g = (- v₀² / 2g) 2/x

a =2  (-v₀² / 2x₀g)  g

therefore the acceleration increases a factor of 2X

3. the initial velocity of the hockey player is v₀ = 20 m / s and the stopping distance is

x = 5cm = 0.05m

we calculate the acceleration

a / g = – 20² / (2 0.05)

a / g = – 4000 / g

a / g = – 4000 / 9.8 = 408

a = 408 g

the correct answer of 400g, the value matches exactly if g = 10 m / s2 is taken