Answer:
t = 3.7 seconds
Step-by-step explanation:
Linear Modeling
The velocity of an object is modeled by the function
v(t) = -78.4t + 288
Where v is expressed in m/s and t is expressed in seconds.
The velocity is a vector, therefore its sign indicates its direction. If the object is at rest, then its velocity has a magnitude of zero.
To find when the object comes to rest, we set the velocity to 0:
-78.4t + 288 = 0
Now solve for t. Subtracting 288:
-78.4t = -288
Dividing by -78.4:
t = -288 / -78.4
t = 3.7 seconds
