Suppose the driver in this example is now moving with speed 38.9 m/s, and slams on the brakes, stopping the car in 4.4 s.
(a) Find the acceleration assuming the acceleration is constant.
(b) Find the distance the car travels, assuming the acceleration is constant.
(c) Find the average velocity.
impatient much?
See your earlier post.
To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is the speed of the driver, which is 38.9 m/s. The final velocity is 0 m/s since the car stops. The time taken to stop the car is 4.4 seconds.
(a) acceleration = (0 m/s - 38.9 m/s) / 4.4 s
= -38.9 m/s / 4.4 s
= -8.84 m/s²
So, the acceleration is approximately -8.84 m/s² (negative because the car is decelerating).
To find the distance the car travels, assuming constant acceleration, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In this case, the initial velocity is 38.9 m/s, and the time is 4.4 seconds.
(b) distance = (38.9 m/s * 4.4 s) + (0.5 * -8.84 m/s² * (4.4 s)^2)
= 171.16 m - 43.3 m
= 127.86 m
So, the car travels approximately 127.86 meters before coming to a stop.
To find the average velocity, we can use the formula:
average velocity = total displacement / total time
In this case, the total displacement is the distance traveled (127.86 m), and the total time is the time taken to stop the car (4.4 seconds).
(c) average velocity = 127.86 m / 4.4 s
= 29.07 m/s
So, the average velocity is approximately 29.07 m/s.