Question

A particle starts from rest and accelerates uniformly for sometime it then stop by uniformly retarding. if the total time of journey is 8 second and retarding is 3 times of acceleration then the time for which it accelerates will be

Answer 1

Heya user !!

Here's the answer you are looking for

See the v-t graph of this particle (see the attachment).

Let the acceleration is a, and it accelerates for time t.

Since, the retardation is 3 times acceleration,
retardation is (-3a) and time is (8-t) (as total time is t)

Let in time t, the particle accelerates to a velocity v.

☛ From the 1st equation of motion,

v = u + at

So, here during acceleration
v = 0 + at
v = at

And during retardation, as it comes to rest, final velocity is 0 and initial is v.
So,
0 = v + (-3a)(8-t)
v = 24a - 3at

☛ From both the equations of v, we get,

at = 24a - 3at

4at = 24a

4t = 24

t = 6

➡️ Therefore, the particle accelerates for 6sec.


★★ HOPE THAT HELPS ☺️ ★★