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An electron moving with a velocity of 5×104ms-1 enters into a uniform electric field and acquires a uniform acceleration of 104ms-2 in the direction of its initial motion (i) Calculate the time in which the electron would acquire a velocity double of its initial velocity. (ii) How much distance the electron would cover in this time?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
(i) The time in which the electron would acquire a velocity double of its initial velocity is 5s.
(ii) The distance the electron would cover in this time is 37.5×104m.
Step 1: Given that
Acceleration acquired by the electron, a=104ms-2
Initial velocity of the electron, u=5×104ms-1
Step 2: Consider the formulae to calculate Distance covered
We can infer the following using the three motion equations:
Distance covered, s=ut+1/2at2,
Where u is the starting speed, t is the travel time, and an is the body’s acceleration.
We also know that,
time, ∆t=v-ua∵a=∆v∆t
Step 3: Now we have to find the time required to double the initial velocity
We require that the final velocity be twice as fast as the initial velocity, thus, v=2u=2×5×104=105ms-1.
We require that the final velocity be twice as fast as the initial velocity is, t=10×104-5×104/104=5s
Step 4: Now we have to find the distance covered
The distance travelled is determined by the first equation by
s=5×104×5+1/2×104×52
On simplifying we get
s=37.5×104m
Therefore,
Five seconds are needed to double the initial velocity.
distance travelled while double the initial velocity is 37.5×104m.
Summary:-
An Electron moving with a velocity of 5×104ms-1 enters into a uniform electric field and acquires a uniform acceleration of 104ms-2 in the direction of its initial motion (i) Calculate the time in which the electron would acquire a velocity double of its initial velocity.(ii) How much distance the electron would cover in this time?
An electron moving with a velocity of 5×104ms-1 enters into a uniform electric field and acquires a uniform acceleration of 104ms-2 in the direction of its initial motion
(i) The time in which the electron would acquire a velocity double of its initial velocity is 5s.
(ii) The distance the electron would cover in this time is 37.5×104m.
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