I am calculating problem by myself and my answer is different after calculation
ID: 1430747 • Letter: I
Question
I am calculating problem by myself and my answer is different after calculation then the answer I have. Am I making somewhere mistake or the answer is wrong?
t2= (10.76 - 112.2a1) / 0.12
t2= 1013 s
for me the answer has too high number or I am making mistake in my calculations and this answer is actually right?
A car starts from rest, and begins accelerating at a constant rate a1. It accelerates at this rate for a distance of 56.1m from its starting point and then immediately begins to decelerate at a different constant rate a2 eventually coming to rest again after traveling an additional distance of 76.9m from where it began decelerating. The entire trip from start to finish (starting and ending at rest) lasts for a duration of 24.7s.
a) What is the magnitude of the initial rate of acceleration, a1?
b) What is the magnitude of the subsequent rate of deceleration, a2?
c) What is the duration of the first part of the trip (the acceleration phase)?
d) What is the duration of the second part of the trip (the deceleration phase)?
e) What is the car's average speed over the course of the entire trip?
Explanation / Answer
trip1
initial velocity , u1=0
acceleration = a1
Distance covered =D1 = 56.1 m
let final velocity after t1 be v1 .
let t1 be the time of this journey
---------------------
trip2
when deceleration starts
a2 is deceleration.
final velocity ,v2 = 0
initial velocity u2 =v1
Distance travelled while decelerating = D2 = 76.9 m
let t2 be time while decelerating.
total time of trip, t = t1 + t2= 24.7 s
---------------------------
using relation v^2 - u^2 = 2aS
for trip1 , v1^2 - 0 = 2 a1 56.1
v1^2 = 112.2 a1 -------------------eq1
similarly for trip 2
v2^2 - v1^2 = 2*a2 * 79.6
0 - 112.2 a1 = 2 *a2 *79.6
a1= 1.42 a2 ---------------------eq2
now, as S =ut1 +0.5*a1*t1^2
56.1 = 0 + 0.5 *a1*t1 ^2
t1 = sqrt (112.2/a1)
similarly fro trip 2
using relation S =D2 = v2*t2 - 0.5 *a2 *t2^2
76.9 = 0 - 0.5 *a2 * t2 ^2
t2 = sqrt ( 153.8/a2)
t1 +t2 = 24.7
sqrt (112.2/a1) + sqrt ( 153.8/a2) = 24.7
sqrt (112.2/1.42 *a2) + sqrt ( 153.8/a2) = 24.76
sqrt(1/a2) [8.89 + 12.4] =24.76
sqrt(1/a2) = 24.7 / 21.29 = 1.16
a2 = 0.743 m/s^2
a1 = 1.055 m/s^2
t1 = sqrt (112.2/a1) = 10.3 sec
t2 = sqrt ( 153.8/a2) = 14.4 sec
as t1 + t2 = 24.7 , IIt seems answer u have in book are correct .
car avg speed = total distance travelled / total time = (56.1 + 76.9)/ 24.7 = 5.385 m/s
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