Given s = 4t + 11t3, find the velocity when t = 1 s.
velocity in m/s =
My Answer:
S'=4+33t^2
=4+33
=4+33
=37
velocity in m/s = 37
Can you please confirm this is correct.
Thank you
S = 4t + 11t^3.
S = 4*1 + 11*1^3 = 4 + 11 = 15 m/s.
NOTE: 1 cubed = 1*1*1 = 1.
oops! I didn't realize you were doing
calculus.
Your calculus is correct.
To find the velocity at a specific time, we need to take the derivative of the equation with respect to time (t).
In this case, we have s = 4t + 11t^3.
To find the derivative, we differentiate each term with respect to t.
The derivative of 4t is 4, as the derivative of t with respect to t is 1.
The derivative of 11t^3 involves using the power rule. The power rule states that if we have t raised to a power (n), the derivative will be n multiplied by t raised to the power (n-1).
In this case, n is 3, so the derivative of 11t^3 is 3 * 11 * t^(3-1) = 33t^2.
Next, we add up the derivatives of each term to find the velocity function, denoted as v(t).
v(t) = 4 + 33t^2.
Now, we can substitute t = 1 into the velocity function to find the velocity at t = 1 second.
v(1) = 4 + 33(1)^2 = 4 + 33(1) = 4 + 33 = 37.
So, the velocity at t = 1 second is indeed 37 m/s.
Therefore, your answer is correct. The velocity at t = 1 s is 37 m/s.