Final answer:
To calculate the car's rate of acceleration, use the kinematic equation to relate displacement, initial velocity, acceleration, and time. Plugging in the given values, the car's acceleration is found to be 4.17 m/s².
Step-by-step explanation:
To determine the rate of acceleration of the car, we can use the kinematic equation that relates initial velocity, acceleration, time, and displacement:
s = ut + ½ at²
where s is the displacement (264 m), u is the initial velocity (45 m/s), a is the acceleration, and t is the time (4.8 s). Rearranging the equation to solve for acceleration a, we get:
a = (2(s - ut)) / t²
Plugging in the known values:
a = 2(264 m - (45 m/s × 4.8 s)) / (4.8 s)²
a = (2(264 m - 216 m)) / 23.04 s²
a = (2(48 m)) / 23.04 s²
a = 96 m / 23.04 s²
a = 4.17 m/s²
Thus, the car's acceleration is 4.17 m/s².