Question

A particle moves along straight line Ox. At time t (seconds) the distance (meters) from 0
is given by: x = 40 + 12t -t³How long the particle travels before coming to rest?​

Answer 1

Answer:

Explanation: the concept of maxima states that if differentiate the expression and equate it with zero it will give us maximum value of that quantity

Answer 2

Given :-

A particle is moving along straight line OX. Postion of the particle = x = 40 + 12t - t³.

We are required to find the distance travelled before coming to rest.

Hence, in this question we will differentiate and find Velocity of the particle and as we know that when a body starts de-accelerating then its velocity will become zero after some time.

Here, differentiating dx w.r.t dt.

v = dx/dt

v = d(40 + 12t - t³)/dt

v = 12 - 3t²

Now, the velocity will become zero.

0 = 12 - 3t²

3t² = 12

t² = 4

t = 2 s

Now, putting the value of 't' in 'x'.

x = 40 + 12 × 2 - 2³

x = 64 - 8

x = 56 m.

Hence,

The distance travelled by body before coming to rest = x = 56 m. Answer......