Question

An ambulance driver is rushing a patient to the hospital. While traveling at 72 km/h, she notices the traffic light at the upcoming intersections has turned amber. To reach the intersection before the light turns red, she must travel 50 m in 2.0 s. (a) What minimum acceleration must the ambulance have to reach the intersection before the light turns red? (b) What is the speed of the ambulance when it reaches the intersectio

Answer 1

(a) The minimum acceleration the ambulance must have is 5 m/s².

(b) The speed of the ambulance when it reaches the intersection is 82 m/s.

(a) To determine the minimum acceleration needed for the ambulance to cover a distance of 50 m in a time of 2.0 seconds, we can use the kinematic equation d=
`v_0t+1/2at^2`, where d is the distance, v_0 is the initial velocity, t is the time, and a is the acceleration. Rearranging the formula to solve for acceleration, we get
`a=2(d-v_0t)/t^2`. Plugging in the values, where d=50 m, v0​=72 km/h converted to 20/9 m/s, and t=2.0 s, we find that the minimum acceleration required is approximately 5 m/s^2.

(b) To find the speed of the ambulance when it reaches the intersection, we can use the kinematic equation v=​v_0 +at, wherev is the final velocity, v_0 is the initial velocity, a is the acceleration, and t is the time. Plugging in the values, where v_0 =72 km/h converted to 20/9 m/s, a=5 m/s^2, and t=2.0 s, we find that the speed of the ambulance when it reaches the intersection is approximately 82 m/s.