A car is traveling to the left, which is the negative direction. The direction o

Question

A car is traveling to the left, which is the negative direction. The direction of travel remains the same throughout this problem. The car's initial speed is 27.0 m/s, and during a 4.6 s interval, it changes to a final speed. In each case, find the acceleration (magnitude and algebraic sign) and whether or not the car is decelerating.

(a) The final speed is 31.8 m/s.
m/s2 and the car is  ---Select--- accelerating decelerating

(b) The final speed is 23.5 m/s.
m/s2 and the car is  ---Select--- accelerating decelerating

Explanation / Answer

According the the kinematic formula

v - u = a*t

Part A)

Given u = -27m/s , v = -31.8 m/s , t = 4.6 m/s

a = v - u/t

a = (-31.8-(-27))/4.6 = -4.8/4.6

= -1.043 m/s^2

The car is acceleration because it is changing it is increasing its speed in the same direction (the negative direction)

Part B) Vf = -23. 5 m/s
Vi = -27 m/s
t = 4.6 s
From the formula,
Vf = Vi + a*t
a = (Vf - Vi)/t
a = (-23.5- (-27))/4.6
a = 0.76 m/s^2

The car is de-accelerating because the acceleration is in the opposite direction of the car's motion.

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