Question

The position of an object is given by the equation . Find the time  at which the instantaneous velocity of the object equals the average velocity in the interval .

Answer 1

Assuming that the correct question is:

The position of an object is given by the equation s(t)=2t²+t-6. Find the time t at which the instantaneous velocity of the object equals the average velocity in the interval [0,3].

Given:

s(t)=2t²+t-6

We know that v(t)=ds(t)/dt

So, v(t)=d(2t²+t-6))/dt

v(t)=4t+1

Now calculating average velocity:

Note: We can also calculate v_avg from the very basic formula:

or by using the formula:

Now we have,

Solving for t from the above equation.

So, at t=1.5s the instantaneous velocity of the object is equal to the average velocity.

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