Final answer:
To determine the initial speed of the car, the kinematic equation s = v0t + (1/2)at^2 was used, where s is the distance, v0 is the initial velocity, a is acceleration, and t is time. After substituting the given values into the equation and solving for v0, the initial speed of the car was found to be 1.598 m/s.
Step-by-step explanation:
To calculate how fast the car was going when it first began to accelerate, we need to use the equations of motion. Given that the car accelerates at 0.0324 m/s² and covers a distance of 1 km (1000 m) in 59.8 seconds, we set this up using the kinematic equation:
s = v0t + ½ at2
Where:
s is the distance traveled (1000 m),
v0 is the initial velocity (what we are solving for),
a is the acceleration (0.0324 m/s²), and
t is the time (59.8 s).
Rearranging this equation to solve for v0, we get:
v0 = (s - ½ at2) / t
Plugging the known values into this formula:
v0 = (1000 m - (½ × 0.0324 m/s² × (59.8 s)2)) / 59.8 s
After calculating, the initial velocity v0 = 1.598 m/s.
Therefore, the correct option is (c) 1.598 m/s.