Question

The maker of an automobile advertises that it takes 7 seconds to accelerate from 30 kilometers per hour to 70 kilometers per hour. assuming constant acceleration, compute the distance, in meters, the car travels during the 7 seconds. round your answer to two decimal places?

a) 385 meters
b) 560 meters
c) 455 meters
d) 630 meters

Answer 1

After converting the speeds from km/h to m/s and using the equations of motion, the calculated distance traveled by the car during the 7 seconds of acceleration is 196.10 meters, which doesn't match the provided options.

Step-by-step explanation:

The question involves calculating the distance traveled by a car during acceleration, assuming constant acceleration. First, we need to convert the speeds from kilometers per hour to meters per second (m/s) and then use the equations of motion to find the distance covered.

Step-by-step solution:

1. Convert 30 km/h to m/s:
   30 km/h × (1000 m/km) × (1 h/3600 s) = 8.33 m/s
2. Convert 70 km/h to m/s:
   70 km/h × (1000 m/km) × (1 h/3600 s) = 19.44 m/s
3. Calculate the acceleration using the formula a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken for acceleration.
   So, a = (19.44 m/s - 8.33 m/s) / 7 s = 1.59 m/s²
4. Use the formula s = v_i * t + (1/2) * a * t² to calculate the distance s traveled during acceleration:
   s = 8.33 m/s * 7 s + (1/2) * 1.59 m/s² * (7 s)²

After performing the calculation, the total distance comes out to be 157.25 m + 38.85 m = 196.10 m, which isn't an option provided in the question. There might be an error in the question's options or the details provided.