Final answer:
Using the formula for uniformly accelerated motion and substituting the known values, the car's acceleration is calculated to be 17.8 m/s².
Step-by-step explanation:
The student's question is asking for the rate of the car's acceleration given that the car, initially traveling at 13.7 m/s, covers 312 meters in 5.2 seconds. To find the acceleration, we can use the formula for uniformly accelerated motion: s = ut + ½ at², where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time. Substituting the known values:
s = ut + ½ at²
312 m = (13.7 m/s)(5.2 s) + ½(a)(5.2 s)²
First, we calculate the initial velocity's contribution to the displacement:
(13.7 m/s)(5.2 s) = 71.24 m
Then, subtract this from the total displacement:
312 m - 71.24 m = 240.76 m
This value is equal to ½(a)(5.2 s)², so we can now solve for a:
240.76 m = ½(a)(5.2 s)²
Multiply both sides by 2 and divide by the square of 5.2 s to isolate a:
a = (2 × 240.76 m) / (5.2 s)²
a = 481.52 m / 27.04 s²
a = 17.8 m/s²
The car's acceleration is therefore 17.8 m/s².