Question

given ( s(t) = t^2 + 3t ), where ( s(t) ) is in feet and ( t ) is in seconds, find each of the following
a) ( v(t) )
b) ( a(t) )
c) the velocity and acceleration when ( t = 2 ) sec

a) ( v(t) = 2t + 3 )
b) ( a(t) = square )

Explanation:

Step1: Recall acceleration is derivative of velocity.

Given \( v(t) = 2t + 3 \), we find \( a(t) \) by differentiating \( v(t) \).

Step2: Differentiate \( v(t) \).

The derivative of \( 2t \) with respect to \( t \) is \( 2 \), and the derivative of \( 3 \) (a constant) is \( 0 \). So \( a(t)=\frac{d}{dt}(2t + 3)=2 \).

Answer:

\( 2 \)