# An ion travelling east through a biological membrane at 150 m/s enters electric field which reduces its velocity to 100m/s towards the east?

An ion travelling east through a biological membrane at 150 m/s enters electric field which reduces its velocity to 100m/s towards the east. While this acceleration (assumed constant) is occurring, the ion undergoes a displacement of 50.0A in the same direction (1 A = 10^-10m)

a) How long did the electric field take to cause this velocity change?

b) What acceleration did the ion experience?

Thank you very much.

Relevance

Ah, there are those magic words "constant acceleration". This is just a kinematics question with a fancy hat on.

I use the suvat symbols. s = displacement; u = initial velocity; v = final velocity; a = acceleration; t = time. You might use different symbols, but you should recognise the form of the equations.

OK I'm calling eastwards the positive direction. My choice.

What do we know here?

s = 50.0A = 50.0 * 10^-10 m

u = 150 m/s

v = 100 m/s

a = ? {Wanted for part (b)}

t = ? {Wanted for part (a)}

(a)

Equation choice

s = ½(u + v)t {The forgotten standard equation. displacement = average velocity * time}

Substitute values

50. 0 * 10^-10 = ½(150 +100)t

t = (50.0 * 10^-10 / 125)

t = 4.00 * 10^-11 seconds

(b)

Equation choice:

v² = u² + 2as {Now I know (t) from part (a), I could just use v = u + at. But I might have fumbled the calculator for (a) and got it wrong :-( }

Substitute values

100² = 150² + 2 * a * 50.0 * 10^-10

a = -1.25 * 10^12 m/s²

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