Final answer:
To determine the time it takes for a car to accelerate from rest to 64 m/s at a rate of 3.2 m/s², use the kinematic equation, resulting in a calculation of 20 seconds.
Step-by-step explanation:
If a car can accelerate from rest at 3.2 m/s² to a final velocity of 64 m/s, we can use the kinematic equation which relates acceleration, initial velocity, final velocity, and time:
Final velocity (v) = Initial velocity (u) + (Acceleration (a) × Time (t))
Since the car starts from rest, the initial velocity (u) is 0 m/s. Using the given acceleration (a) of 3.2 m/s² and the final velocity (v) of 64 m/s, we can solve for time (t).
64 m/s = 0 m/s + (3.2 m/s² × t)
Now, we rearrange to solve for time (t):
t = (64 m/s) / (3.2 m/s²) = 20 s
Therefore, it will take the car 20 seconds to accelerate from rest to 64 m/s, which corresponds to option (b).