Question

2. The velocity of an object in motion is given by the function y(t)=-78.4t + 288 where vt is the velocity of the object in meters per second at time t.

B. After how many seconds does the object momentarily come to rest and then change directions?​

Answer 1

t = 3.7 seconds

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