# 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.

### 1 Answer

- 8 months agoFavourite answer
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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