Question

An electron has an initial speed of 1.32 × 105 m/s. If it undergoes an acceleration of 1.8 × 1014 m/s 2, how long will it take to reach a speed of 7.76 × 105 m/s? Answer in units of s. How far has it traveled in this time? Answer in units of m.

Answer 1

Here ,

initial speed , u = 1.32 *10^5 m/s

accelearation , a = 1.8 *10^14 m/s^2

final speed , v = 7.76 *10^5 m/s

let the time taken is t

Using first equation of motion

v = u + a * t

7.76 *10^5 = 1.8 *10^14 * t + 1.32 *10^5

solving for t

t = 3.58 *10^-9 s

the time taken is 3.58 *10^-9 s

let the distance travelled is d

Using third equation of motion

v^2 - u^2 = 2 * a * s

(7.76 *10^5)^2 - ( 1.32 *10^5)^2 = 2 ( 1.8 *10^14) * s

s = 1.62 *10^-3 m

electron has travelled about 1.62 *10^-3 m