Question

2. For timet> 0 in seconds, a police car is patrolling a local street. The position along

the straight, flat road is given in meters by the function P(t)=25t. Directly ahead
of the police car, a bank robber's getaway car begins to speed up to leave the scene
of the crime. The getaway car's position along the road is given in meters by the
function G(t)=75+2.5. Graph the functions P and G on the same set of axes. What
conclusion can you draw? Does the police car catch the getaway car? Determine the
time at which the police car intersects the getaway car, or determine how close the
police car gets to the getaway car before the bank robber evades capture.

Answer 1

The position of the police car along the road is given by the function P(t) = 25t. The position of the getaway car along the road is given by the function G(t) = 75 + 2.5t.

To determine if and when the police car intersects with the getaway car, we can set P(t) equal to G(t) and solve for t: P(t) = G(t) 25t = 75 + 2.5t 22.5t = 75 t = 3.33 seconds

So, after approximately 3.33 seconds, the police car will intersect with the getaway car.