Questions: Given s(t)=t+3, where s(t) is in miles and t is in hours, find each of the following. a) v(t) b) a(t) c) The velocity and acceleration when t=2 hr d) When the distance function is given by a linear function, there is uniform motion. What does uniform motion mean in terms of velocity and acceleration?

Given s(t)=t+3, where s(t) is in miles and t is in hours, find each of the following.
a) v(t)
b) a(t)
c) The velocity and acceleration when t=2 hr
d) When the distance function is given by a linear function, there is uniform motion. What does uniform motion mean in terms of velocity and acceleration?

Transcript text: Given $s(t)=t+3$, where $s(t)$ is in miles and $t$ is in hours, find each of the following. a) $v(t)$ b) $a(t)$ c) The velocity and acceleration when $\mathrm{t}=2 \mathrm{hr}$ d) When the distance function is given by a linear function, there is uniform motion. What does uniform motion mean in terms of velocity and acceleration?

Solution

Solution Steps

Step 1: Determine the Velocity Function $ v(t) $

To find the velocity function $ v(t) $, we take the derivative of the distance function $ s(t) = t + 3 $ with respect to time $ t $. The derivative of $ t + 3 $ is:

\[ v(t) = \frac{d}{dt}(t + 3) = 1 \]

Step 2: Determine the Acceleration Function $ a(t) $

The acceleration function $ a(t) $ is the derivative of the velocity function $ v(t) $. Since $ v(t) = 1 $, the derivative is:

\[ a(t) = \frac{d}{dt}(1) = 0 \]

Step 3: Calculate the Velocity and Acceleration at $ t = 2 $ hours

Substitute $ t = 2 $ into the velocity and acceleration functions: