a particle starts 4m rest n moves with constant acceleration of P m/s2 4 smtime it than de-accelerates uniformly - Physics - Motion In A Straight Line

Question

a particle starts 4m rest n moves with constant acceleration of
P m/s2 4 smtime it than de-accelerates uniformly at a rate of Q
m/s2 4 smtime and fnlly stops it remains in motion 4 time T PT the
distance travelled by the particle is [PQT2/P+Q]

Panchali Dutta · Accepted Answer

The body starts from rest, that is, u = 0 m/s

Let the distance travelled and final velocity at time t₁ be s m and v m/s respectively.

Using laws of motion,

$v = u + P t_{1} \Rightarrow t_{1} = v / P v^{2} = u^{2} + 2 P s_{1} \Rightarrow s_{1} = v^{2} / 2 P$

The final velocity of the body is zero.

Let the distance travelled in time t₂ be s₂ m.

Initial velocity of the body = final velocity of the body at t₁ = v m/s

Similarly,

$t_{2} = v / Q a n d s_{2} = v^{2} / 2 Q$

total time for the body in motion, T = t₁ + t₂

$\Rightarrow T = v [\frac{1}{P} + \frac{1}{Q}] \Rightarrow v = \frac{P Q T}{P + Q}$

Total distance travelled, s = s₁ + s₂

$s = v^{2} [\frac{1}{P} + \frac{1}{Q}] \Rightarrow s = \frac{P Q T^{2}}{2 (P + Q)}$

a particle starts 4m rest n moves with constant acceleration of P m/s2 4 smtime. it than de-accelerates uniformly at a rate of Q m/s2 4 smtime and fnlly stops. it remains in motion 4 time T. PT the distance travelled by the particle is [PQT2/P+Q]

a particle starts 4m rest n moves with constant acceleration of P m/s2 4 smtime. it than de-accelerates uniformly at a rate of Q m/s2 4 smtime and fnlly stops. it remains in motion 4 time T. PT the distance travelled by the particle is [PQT²/P+Q]