Sladerthe position s(t) of a particle moving along the x-axis at time t is given by s(t) = −t3 + 3t2 + 5 4 , where s is measured in meters and t is measured in seconds. at what time is the particle's instantaneous velocity equal to its average velocity on the interval [0, 6]?

t = 3.646 seconds

Step-by-step explanation:

We have given instantaneous velocity

Now,

Now we will find the average velocity

It is also given that particle's instantaneous velocity equal to its average velocity.

From equation (1) and (2)

Now we factorize the equation by the rule of Shri dharacharya

If we put the value of

If we take positive value than

t = 1 + 2.646 = 3.646

If we take negative value than

t = 1 - 2.646 =  -1.646

We can not take negative value of time So, t = 3.646 seconds