Answer:
Explanation:
To calculate the acceleration of a car from 70 mph to 50 mph over a distance of 100 meters, we can use the following steps:
Convert the speeds from miles per hour (mph) to meters per second (m/s). We can do this by multiplying the speeds by 0.44704, which is the conversion factor between mph and m/s:
Initial speed: 70 mph x 0.44704 = 31.2928 m/s
Final speed: 50 mph x 0.44704 = 22.352 m/s
Calculate the change in velocity (Δv) by subtracting the final speed from the initial speed:
Δv = 22.352 m/s - 31.2928 m/s = -8.9408 m/s
Note that the change in velocity is negative because the car is slowing down.
Calculate the distance traveled during the deceleration by using the formula:
d = (v_f^2 - v_i^2) / (2a)
where d is the distance, v_f is the final velocity, v_i is the initial velocity, and a is the acceleration.
In this case, we know d = 100 meters, v_f = 22.352 m/s, and v_i = 31.2928 m/s. We can rearrange the formula to solve for a:
a = (v_f^2 - v_i^2) / (2d)
a = (22.352^2 - 31.2928^2) / (2 x 100)
a ≈ -2.84 m/s^2
Again, the acceleration is negative because the car is decelerating.
Therefore, the acceleration of the car from 70 mph to 50 mph over a distance of 100 meters is approximately -2.84 m/s^2.