Question

The position x of a particle with respect to time t along x-axis is given by x=9t2–t3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

Answer 1

Answer:

the correct answer is 54m

Explanation:

Given that,

x=9t  

2

−t  

3

.....(I)

We know that,

v=  

dt

dx

​  

 

The maximum speed is

v=18t−3t  

2

 

v maximum, at  

dt

dv

​  

=0

dt

dv

​  

=18−6t

The time will be

0=18−6t

t=3 sec

The position of the particle at 3 sec

Put the value of t in equation (I)

x=9×9−27

x=81−27

x=54 m

The position of the particle will be 54 m.

Hence, Option A is correct

Answer 2

Question: The position x of a particle with respect to time t along x-axis is given by x=9t2–t3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

Answer:

54 m (option a)