problem 2.26\nthe driver of a car traveling on the highway suddenly slams on the brakes because of a…

problem 2.26\nthe driver of a car traveling on the highway suddenly slams on the brakes because of a slowdown in traffic ahead.\na) if the cars speed decreases at a constant rate from 34 m/s to 20 m/s in 3.0 s, what is the magnitude of its acceleration, assuming that it continues to move in a straight line?\nb) what distance does the car travel during the braking period?

problem 2.26\nthe driver of a car traveling on the highway suddenly slams on the brakes because of a slowdown in traffic ahead.\na) if the cars speed decreases at a constant rate from 34 m/s to 20 m/s in 3.0 s, what is the magnitude of its acceleration, assuming that it continues to move in a straight line?\nb) what distance does the car travel during the braking period?

Answer

Explanation:

Part a:

Step1: List known values

( v_i = 34 , \text{m/s}, v_f = 20 , \text{m/s}, t = 3.0 , \text{s} )

Step2: Calculate velocity change

( \Delta v = v_f - v_i = 20 - 34 = -14 , \text{m/s} )

Step3: Compute acceleration magnitude

( |a| = \left| \frac{\Delta v}{t} \right| = \left| \frac{-14}{3.0} \right| \approx 4.7 , \text{m/s}^2 )

Part b:

Step1: Calculate average velocity

( v_{avg} = \frac{v_i + v_f}{2} = \frac{34 + 20}{2} = 27 , \text{m/s} )

Step2: Compute braking distance

( d = v_{avg} \times t = 27 \times 3.0 = 81 , \text{m} )

Answer:

a) 4.7 m/s² b) 81 m