Using the acceleration function below, find the velocity function, if the velocity is v = 5 at time t = 2.
$a\left(t\right)=-20$

• A. $v\left(t\right)=-20t+10$
• B. $v\left(t\right)=-20t+5$
• C. $v\left(t\right)=-20t+45$
• D. $v\left(t\right)=-20t-35$

Answer: (C)

Verified step by step guidance

1. Start by understanding that the acceleration function a(t) = -20 is a constant. This means the velocity function v(t) is the antiderivative of a(t).
2. To find the velocity function v(t), integrate the acceleration function a(t) with respect to time t. The integral of a constant -20 with respect to t is -20t plus a constant of integration, C.
3. The general form of the velocity function after integration is v(t) = -20t + C, where C is a constant that we need to determine.
4. Use the initial condition given in the problem: v = 5 at t = 2. Substitute these values into the velocity function to solve for C: 5 = -20(2) + C.
5. Solve the equation 5 = -40 + C to find the value of C. Once C is determined, substitute it back into the velocity function to get the specific velocity function v(t).