PLEASE USE FORMULAS AND BOX YOUR ANSWERS.Thanks! Section 2 A car starts from res

Question

PLEASE USE FORMULAS AND BOX YOUR ANSWERS.Thanks!

Section 2

A car starts from rest, and begins accelerating at a constant rate a1 . it accelerates at this rate for a distance of 30.2m 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 40.5m from where it began decelerating. The entire trip from start to finish (Starting and ending at rest) lasts for a duration of 28.0s

A) what is the duration of the first part of the trip (the acceleration phase)? _________._____ s

B) what is the duration of the second part of the trip (the deceleration phase)? ________.______s

C)what is the car's average speed over the course of the entire trip? ________._____ m/s

D) what is the magnitude of the initial rate of acceration, a1? _________.______ m/s2

E) what is the magnitude of the subsequent rate of deceleration, a2? ________._______ m/s2

Explanation / Answer

for accelaration

initial speed is Vo = 0 m/sec

accelaration is a1 =

distance travelled is S1 = 30.2 m

then using

S1 = (Vo*t)+(0.5*a1*t1^2)

30.2 = (0*t)+(0.5*a1*t1^2)

30.2 = 0.5*a1*t1^2 ..........(1)

a1*t1^2 = 60.4

a1 = 60.4/t1^2

for deccelaration

initial velocity is V = Vo+(a1*t1) = 0+(a1*t1) =a1*t1

final velocity is V1 = 0 m/sec

S2 = 40.5 m

then using

V1^2 -V^2 = -2*a2*S2

0^2 - (a1*t1^2) = -2*a2*40.5
a1*t1^2 = 2*a2*40.5

a2 = a1*t1^2/(81)

also using

S2 = (V*t2)-(0.5*a2*t2^2)

40.5 = (a1*t1*t2)-(0.5*a2*t2^2)

given that t1+t2 = 28 sec

t2 = 28-t1

then

40.5 = (a1*t1*(28-t1)) - (0.5*(a1*t1^2/81)*(28-t1)^2)..........(2)

40.5 = (28*a1*t1 - 60.4) - (0.5*(60.4/81)*(28-t1)^2

40.5 = (28*a1*t1 - 60.4) - (0.372*(28-t1)^2)

a1*t1 = 60.4/t1

40.5 = ((28*60.4/t1) - 60.4) - (0.372*(28-t1)^2)

solving we get t1 = 6 sec is the answer for a)

B) t2 = 28-t1 = 28-6 = 22 sec

C) avearge speed is Vavg = total distance travelled / total time taken= (40.5+30.2)/28 = 2.525 m/sec

D) a1*t1^2 = 60.4

a1*6^2 = 60.4

a1 = 1.67 m/s^2

E) a2 = a1*t1^2/(81) = 1.67*6^2/81 = 0.74 m/s^2

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