Question

The acceleration of a particle depends on the velocity as a = kv at t = 0, x = 0 and v = 1 m/s. Find position of the particle as a function of time.

Class: 11
Chapter: Motion in a straight line

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Answer 1

Answer:

Given a=kv

d(v) /dt=kv

d(v) /v=k.dt

{d(v) /v = {k.dt

1. logv=kt+c
2. put v=1 and t=0
3. then c=0
4. logv=kt
5. v=e'kt
6. dc/dt=e'kt
7. dx=e'kt.dt
8. {dx={e'kt.dt
9. x=e'kt/k+c'
10. put x=0 and t=0
11. c'=-1
12. Hence X=e'kt/k -1 ans