Question

the position of the particle varies as x=16t -t^2. Find the maximum displacement in the positive direction​

Answer 1

Answer:

Given:

Position of an object varies as

x = 16t - t²

To find:

Maximum displacement in positive direction. In other words, we have to find the maximum positive value of "x".

Concept:

In order to find maximum value for any function, follow these rules.

1. let the function be f(x).

2. Find out values of x for which f'(x) is zero.

3. Maximum value will be obtained for that value of x in which f"(x)<0.

Calculation:

f(t) = 16t - t²

so , f'(t) = 16 -2t = 0

=> 2t = 16

=> t = 8.

Now, f"(t) = -2 , which is less than 0.

So Maxima will be obtained when t = 8.

So maximum value for "x"

x = 16 × 8 - 8²

=> x = 128 - 64

=> x = 64.

So the answer is 64.

Answer 2

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↪Refer the attachment.