X(t)= 0.0945t^4 - 0.171^3 + 0.751^2 +4.53t -6.07
find the acceleration if t= 2.77s

The acceleration at t = 2.77 s is 7.36 m/s².

Explanation:

As we know that acceleration is determined by the rate of change in velocity and velocity is determined as the rate of change in distance. So indirectly, acceleration can also be determined as the second order differentiation of distance.

Such as and

So,

As here the x is given as function of t as

So first to determine the velocity, we have to differentiate the above function with respect to t, and the answer is

Now, to find the acceleration, we have to again differentiate this with respect to t. So the final answer is

So as the time is given as t = 2.77 s, substitute this in above equation, to determine the acceleration at this time. So the answer will be

a=8.701-2.842+1.501=7.36 m/s².

Thus, the acceleration at t = 2.77 s is 7.36 m/s².