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

To avoid running a red light, the minimum acceleration required by the ambulance is 5 m/s², and its speed when reaching the intersection will be 30 m/s.

Step-by-step explanation:

Calculating Acceleration and Final Speed

To answer question 90 regarding the ambulance driver facing a traffic light situation:

(a) Required Acceleration

To find the minimum acceleration the ambulance must have to reach the intersection in 2.0 seconds, we use the formula:
s = ut + ½at²

Where:

s is the distance (50 m)

u is the initial velocity (72 km/h, which is 20 m/s)

t is the time (2.0 s)

a is the acceleration (which we want to find)

Rearranging for a, we have:

a = 2(s - ut) / t²

Plugging in the numbers:

a = 2(50 m - 20 m/s × 2.0 s) / (2.0 s)²

a = 2(50 m - 40 m) / 4.0 s²

a = 2(10 m) / 4.0 s²

a = 20 m / 4.0 s²

a = 5 m/s²

The minimum acceleration needed is 5 m/s².

(b) Final Velocity of the Ambulance

To find the velocity of the ambulance when it reaches the intersection, we use the formula:
v = u + at

Where:

v is the final velocity

u is the initial velocity (20 m/s)

a is the acceleration (5 m/s²)

t is the time (2.0 s)

Plugging in the numbers:

v = 20 m/s + 5 m/s² × 2.0 s

v = 20 m/s + 10 m/s

v = 30 m/s

The ambulance's speed when it reaches the intersection is 30 m/s.

Answer 2

(a) The minimum acceleration required is 5 m/s².

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

To determine the minimum acceleration needed for the ambulance to reach the intersection before the traffic light turns red, we can use the kinematic equation d=ut+ 1/2 at^2, where d is the distance, u is the initial velocity, t is the time, and a is the acceleration. In this case, the ambulance needs to cover a distance of 50 m in 2.0 seconds with an initial speed of 72 km/h. Converting the speed to meters per second (20m/s), we can rearrange the formula to solve for acceleration (a), yielding a minimum acceleration of 5m/s^2.

Next, to find the speed of the ambulance when it reaches the intersection, we use the kinematic equation v=u+at, where v is the final velocity. With the determined acceleration of 5m/s^2 and the initial velocity of 20m/s, we find that the speed of the ambulance when it reaches the intersection is 82m/s. These calculations demonstrate the relationship between acceleration, initial speed, and distance traveled, providing crucial information for the ambulance driver to reach the intersection before the traffic light turns red.