Final answer:
To find the time it takes to accelerate from 30 m/s to 76 m/s at an acceleration of 6 m/s², use the formula ∆t = ∆v / a. The change in velocity is 46 m/s and when divided by the acceleration, the time is approximately 7.67 seconds, which rounds up to 8 seconds.
Step-by-step explanation:
To calculate the time it takes for an object to accelerate from one speed to another, we can use the formula for acceleration, which is a = ∆v / ∆t, where a is the acceleration, ∆v is the change in velocity, and ∆t is the change in time.
In the given question, the initial velocity (v_i) is 30 m/s west, the final velocity (v_f) is 76 m/s west, and the acceleration (a) is 6 m/s² west. To find the time (∆t), we rearrange the formula to solve for ∆t: ∆t = ∆v / a. We calculate the change in velocity as ∆v = v_f - v_i = 76 m/s - 30 m/s = 46 m/s.
Plugging the values into the formula, we get ∆t = 46 m/s / 6 m/s² = 7.67 s. Since we don't have an option for 7.67 seconds, we round up to the nearest whole number, which is 8 seconds (Option C).