Q-8 A particle is moving along a straight line and its position is given by the relation x=t3-6t2-15t+40 m - Physics - Motion In A Straight Line

Question

Q-8 A particle is moving along a straight line and its position is
given by the relation x = t 3 - 6 t 2 - 15 t + 40   m Find
a) The time at which velocity is zero
b) Position and displacement of the particle at that point
c) Acceleration for the particle at that line

Rahul Vyas · Accepted Answer

d(x)=
d(t3-6t2-15t+40)
d(t) d(t)
It is given that d(x)=v=0
d(t)
After differentiating,
3t​2-12t-15=0
t= -1(not applicable),5
Therefore, t=5 seconds

At x={(5)3-6(5)2-15(5)+40}
x=125-150-75+40
=60m in the opposite diection

​a=d(v)=d(3t​2-12t-15)

d(t) d(t)
=6t-12
At t=5sec,
=6(5)-12=18ms​-2

Q-8. A particle is moving along a straight line and its position is given by the relation x = t 3 - 6 t 2 - 15 t + 40 m . Find a) The time at which velocity is zero. b) Position and displacement of the particle at that point. c) Acceleration for the particle at that line.

Q-8. A particle is moving along a straight line and its position is given by the relation $x = (t^{3} - 6 t^{2} - 15 t + 40) m$ . Find
a) The time at which velocity is zero.
b) Position and displacement of the particle at that point.
c) Acceleration for the particle at that line.