Question

A proton in a uniform electric field moves along a straight line with constant acceleration. Starting from rest it attains a velocity of 1,000,000 m/s in a distance of 0.01 m. a.) What is the acceleration? b.) What time is required to reach the given velocity?

Answer 1

a) The acceleration of the proton is $5.0\cdot 10^{13} m/s^2$

b) The time required to reach the given velocity is $2\cdot 10^{-8}s$

Explanation:

a)

This is a motion at constant acceleration, so we can use the following suvat equation:

$v^2-u^2=2as$

where

v is the final velocity

u is the initial velocity

a is the acceleration

s is the distance covered

For the proton in this problem, we have:

$v=1,000,000 m/s$ is the final velocity

$u=0$ is the initial velocity (it starts from rest)

$s = 0.01 m$ is the distance covered

Solving for a, we find the acceleration:

$a=\frac{v^2-u^2}{2s}=\frac{(1,000,000)^2-0}{2(0.01)}=5.0\cdot 10^{13} m/s^2$

b)

For this part, we can use the following suvat equation instead:

$v=u+at$

where:

v is the final velocity

u is the initial velocity

a is the acceleration

t is the time taken for the velocity to change from u to v

We have here the following data:

$v=1,000,000 m/s$ is the final velocity

$u=0$ is the initial velocity (it starts from rest)

$a=5.0\cdot 10^{13} m/s^2$

Solving for t, we find

$t=\frac{v-u}{a}=\frac{1,000,000}{5.0\cdot 10^{13}}=2\cdot 10^{-8}s$

Learn more about accelerated motion here:

brainly.com/question/9527152

brainly.com/question/11181826

brainly.com/question/2506873

brainly.com/question/2562700

#LearnwithBrainly