ppose 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.
(a) 38.9 + 4.4a = 0, so a = -8.84 m/s^2
(b) s(t) = 38.9t + 1/2 at^2
(c) avg v is (38.9+0)/2
To find the answers to these questions, we need to use the formulas of motion:
(a) To find the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 38.9 m/s, the final velocity (v) is 0 m/s (since the car comes to a stop), and the time (t) is 4.4 s, we can substitute these values into the formula:
acceleration = (0 - 38.9) / 4.4
Simplifying this equation gives:
acceleration = -8.84 m/s²
So, the acceleration assuming it is constant is -8.84 m/s² (negative because the car is decelerating).
(b) To find the distance the car travels, assuming constant acceleration, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Substituting the given values into the equation:
distance = (38.9 * 4.4) + (0.5 * -8.84 * 4.4^2)
Simplifying this equation gives:
distance = 170.7568 meters
So, the car travels a distance of approximately 170.76 meters.
(c) The average velocity is defined as the total displacement divided by the total time taken. Since the car comes to a stop, the total displacement is equal to the distance traveled.
average velocity = distance / time
Substituting the values:
average velocity = 170.7568 / 4.4
Simplifying this equation gives:
average velocity = 38.81 m/s
So, the average velocity is approximately 38.81 m/s.