Question
The position of a particle travelling along x - axis is given by xt = t3 - 9 t2 + 6t where xt is in m and t is in second . Then
1) the particle does not come to rest at all.
2) the particle comes to rest firstly at (3 - √7 ) s and then at (3 + √7) s
3) the speed of the particle at t= 2s is 18 ms−1
4) the acceleration of the particle at t= 2s is 6 ms−2
1) the particle does not come to rest at all.
2) the particle comes to rest firstly at (3 - √7 ) s and then at (3 + √7) s
3) the speed of the particle at t= 2s is 18 ms−1
4) the acceleration of the particle at t= 2s is 6 ms−2
Answer: Option A
:
A
xt = t3 - 9 t2 + 6t
v= dxtdt = (3 t2 - 18t + 6) m s−1
So, the particlecomes to rest since this equation has two valid roots.
⇒ t1 =(3 - √7) s and ⇒ t2 =(3 - √7) s
Substituting the value t = 2s in the equation for velocity, we get, v= = - 18ms−1
The acceleration of the particle is a=6t - 18ms−2
Substituting the value t = 2s in the equation for acceleration, we get, a= = - 6ms−2
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:
A
xt = t3 - 9 t2 + 6t
v= dxtdt = (3 t2 - 18t + 6) m s−1
So, the particlecomes to rest since this equation has two valid roots.
⇒ t1 =(3 - √7) s and ⇒ t2 =(3 - √7) s
Substituting the value t = 2s in the equation for velocity, we get, v= = - 18ms−1
The acceleration of the particle is a=6t - 18ms−2
Substituting the value t = 2s in the equation for acceleration, we get, a= = - 6ms−2
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