1. A sports car travelling east at 48.0 m/s passes a trooper hiding at the roadside. The driver uniformly reduces his speed to 22 m/s in 4.10 s
a) Find the magnitude and direction of the car’s acceleration as it slows down
b) Calculate the distance traveled during the 4.10 s time interval
(a) a = [(22 - 48)m/s]/4.1s
= -6.3 m/s^2
(b) X = Vaverage*(4.1s) = 35 m/s*4.1s
= 143.5 m
can i know how to get Vaverage?
Vav is the average of the initial and final velocities during deceleration.
It equals (Vinitial + Vfinal)/2
To find the magnitude and direction of the car's acceleration, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
In this case:
Initial velocity (u) = 48.0 m/s
Final velocity (v) = 22.0 m/s
Time (t) = 4.10 s
Substituting these values into the formula, we get:
acceleration = (22.0 m/s - 48.0 m/s) / 4.10 s
Simplifying this, we get:
acceleration = -26.0 m/s / 4.10 s
Therefore, the car's acceleration is -6.34 m/s^2 (rounded to two decimal places). The negative sign indicates that the car is decelerating, or slowing down.
To calculate the distance traveled during the 4.10 s time interval, we can use the formula for average velocity:
average velocity = total displacement / total time
Since the car is slowing down, the average velocity will be the average of the initial and final velocities:
average velocity = (initial velocity + final velocity) / 2
Substituting the given values, we get:
average velocity = (48.0 m/s + 22.0 m/s) / 2 = 35.0 m/s
To find the total displacement, we can use the formula:
total displacement = average velocity * total time
Substituting the values we have:
total displacement = 35.0 m/s * 4.10 s
Calculating the result:
total displacement = 143.5 m
Therefore, the car traveled a distance of 143.5 meters during the 4.10 s time interval.