Question

given s(t) = t² + 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) = 2 c) when t = 2 sec, the velocity is 7 ft/sec. (simplify your answer.) when t = 2 sec, the acceleration is (simplify your answer.)

Explanation:

Step1: Recall acceleration function

From part (b), \( a(t) = 2 \). This is a constant function, so its value does not depend on \( t \).

Step2: Evaluate at \( t = 2 \)

Since \( a(t) \) is constant (\( a(t)=2 \) for all \( t \)), when \( t = 2 \), \( a(2)=2 \).

Answer:

2 ft/s² (Note: The unit for acceleration here, since the position is in feet and time in seconds, the acceleration unit is feet per second squared. But the numerical value is 2.)