Final answer:
To determine the time it takes for the car to reach 33.0 m/s from an initial velocity of 4.0 m/s with an acceleration of 3.0 m/s^2, the formula t = (v - u) / a is used, resulting in a time of 9.67 seconds.
Step-by-step explanation:
The question given refers to a situation in which a car has an initial velocity of 4.0 m/s when it begins to be accelerated at 3.0 m/s2. To find out how long it takes to reach a velocity of 33.0 m/s, we can use the formula for acceleration, which is a = (v - u) / t, where 'a' is acceleration, 'v' is the final velocity, 'u' is the initial velocity, and 't' is time.
Using the given data:
a = 3.0 m/s2, u = 4.0 m/s, and v = 33.0 m/s, we can rearrange the formula to solve for 't': t = (v - u) / a. Plugging in the values gives us t = (33.0 m/s - 4.0 m/s) / 3.0 m/s2, which simplifies to t = 29.0 m/s / 3.0 m/s2 = 9.67 seconds. Therefore, the correct answer is (d) 9.67 seconds.