An object moves along a straight line so that at any time t , for 0≤t≤8 , its position is given by x(t)=5+4t−t2 . For what value of t is the object at rest?
A. t = 2
B. t = 4
C. t = 9/2
D. t = 5

Answer:

D. t = 5

when the object is at rest => x(t) = 0

<=> -t^2 + 4t + 5 = 0

<=> t^2 - 4t - 5 = 0

<=> (t - 5)(t + 1) = 0

=> t = 5 or t = -1

but t》0

=> t = 5

The value of t if the object at rest is 2 secs: Option A is correct

Given the position of the object moving in a straight line expressed as:

x(t)=5+4t−t²

The velocity of the body at rest is zero

Get the velocity fucntion.

v(t) = d(x(t))/dt = 4 - 2t

Since v(t) = 0

0 = 4 - 2t

-4 = -2t

t = 2

Hence the value of t if the object at rest is 2 secs

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