Final answer:
To find the distance the ambulance must travel to reach the car's velocity, we use the kinematic equation s = (v² - u²) / (2a). Upon calculation, the distance comes out to be 67.5 meters, with the closest answer choice being 70 meters.
Step-by-step explanation:
The question asks how far an ambulance with a constant acceleration of 5 m/s² must travel to match the velocity of a car moving at a constant velocity of 30 m/s, given that the ambulance is currently traveling at 15 m/s. To determine this, we need to use the kinematic equations for motion.
We know that the final velocity (v) the ambulance needs to reach is 30 m/s, it starts with an initial velocity (u) of 15 m/s, and it accelerates at a = 5 m/s². We can use the equation v² = u² + 2as, where s is the distance. Rearranging the equation to solve for s gives us:
s = (v² - u²) / (2a)
Plugging in the values:
s = (30² - 15²) / (2 * 5)
s = (900 - 225) / 10
s = 675 / 10
s = 67.5 meters
The closest answer choice to 67.5 meters is 70 meters (d).