Question

Consider that the position of an object is given by the following equation :

$s(t) = 2te^{t}$ Will this object stop moving? If so, at which value of t the object will stop moving.


please provide an explanation with the answer

Answer 1

Answer:

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Step-by-step explanation:

We will solve this by differentiation,

d/dt(2te^t)=e^t(d/dt2t)+2t(d/dt e^t)

As ds/dt is equal to velocity,

So, v=2e^t+2te^t

v=e^t(2+2t)

as we know the v=0 if object stops moving,

0=e^t(2+2t)

0=2+2t

2t=-2

t=-1 which is not possible

So, the object will not stop moving.

Answer 2

From the given question the correct answer is the object will not stop moving.

Solution:

We will solve this by differentiation,

d/dt(2te^t)=e^t(d/dt2t)+2t(d/dt e^t)

As ds/dt is equal to velocity,

So, v=2e^t+2te^t

v=e^t(2+2t)

as we know the v=0 if object stops moving,

0=e^t(2+2t)

0=2+2t

2t=-2

t=-1 which is not possible

So, the object will not stop moving.