Question

A particle starts with initial speed v1 and travels along a straight line with an acceleration a = cv m/s2, where v is in m/s and c is a positive constant. what is the distance traveled by the particle before its speed reaches v2?

Answer 1

To find the distance traveled by the particle before its speed reaches v2, we need to find the time it takes for the particle to reach v2 and then use the equation for distance traveled with constant acceleration.

Step-by-step explanation:

The acceleration of a particle is given by the equation a = cv, where c is a positive constant and v is the velocity. To find the distance traveled by the particle before its speed reaches v2, we need to find the time it takes for the particle to reach v2 and then use the equation for distance traveled with constant acceleration:

d = v1t + 1/2at2

where v1 is the initial velocity, a is the acceleration, and t is the time. Let's solve step by step:

1. Find the time it takes for the particle to reach v2 using the equation v = u + at, where u is the initial velocity and a is the acceleration.
2. Once the time is found, substitute it into the equation d = v1t + 1/2at2 to find the distance traveled.

Answer 2

Explanation :

It is given that,

initial speed of particle is
`v_1`

final speed of particle is
`v_2`

acceleration of particle is
`a=cv`

Let s is the distance traveled by particle before it reaches
`v_2`

Now, using equation of motion as :

`v^2_2-v^2_1=2as`

so,
`s=(v^2_2-v^2_1)/(2a)`

`s=(v^2_2-v^2_1)/(2cv)`

Hence, the distance covered by the particle is
`s=(v^2_2-v^2_1)/(2cv)`