Final answer:
The appropriate acceleration the ambulance would need to reach the intersection in 2 s is 5.0 m/s², which is not listed among the provided options. The speed of the ambulance upon reaching the intersection would be 108 km/h, also not matching the options given.
Step-by-step explanation:
The student's question involves determining the required acceleration for an ambulance to reach an intersection and its speed upon reaching it while considering its initial speed and a certain distance to be covered in a given time. To solve this, we can use the kinematic equations of motion.
Part (a): Calculate Minimum Acceleration
To find the minimum acceleration that the ambulance must have to cover 50 m in 2.0 s, we'd use the kinematic equation:
v = u + at
Where:
• v is the final velocity (which we don't yet know)
• u is the initial velocity = 72 km/h = 20 m/s (converted from km/h to m/s)
• a is the acceleration (which we're trying to find)
• t is the time = 2.0 s
First, we need to determine the final velocity (v) the ambulance would reach after 2.0 seconds if it continued at the initial speed without acceleration:
v = u + (0 × t) = 20 m/s
Now, using the equation s = ut + (1/2)at², where s is the distance (50 m), we can plug in the known values and solve for a:
50 = (20 × 2) + (1/2)a(2)^2
50 = 40 + 2a
a = (50 - 40) / 2
a = 5 m/s²
Part (b): Calculate Speed at the Intersection
The speed of the ambulance when it reaches the intersection, having accelerated at 5 m/s² for 2.0 s, can be found using the initial equation:
v = u + at
v = 20 m/s + (5 m/s² × 2.0 s)
v = 20 m/s + 10 m/s
v = 30 m/s
To convert this back to km/h, multiply by 3.6:
30 m/s × 3.6 = 108 km/h
Thus, the correct option for the acceleration and speed of the ambulance at the intersection would be option not given in the list: 5.0 m/s², 108 km/h.