Can anyone confirm the answer I have to this question?

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Total time: 225 sec
Total distance travelled: 8100 m
Speed: 36 m/s

2 Answers
Feb 4, 2017

Given

For first phase journey

#u_1-> "initial velocity of the car "=0#
#t_1->"duration of first phase journey"=15s#
#a_1->"uniform acceleration in first phase"=2.4ms^-2#

So applying kinematic equation #s=ut+1/2at^2#
we get distance traversed in first phase

#s_1=u_1xxt_1+1/2xxa_1xxt_1^2#

#=>s_1=0xx2.4+1/2xx2.4xx15^2=270m#

For Second phase journey

At the end first phase it will acquire velocity #v_2# which will be initial velocity for second phase journey.

So #v_2=u_1+a_1xxt_1=0xxt_1+2.4xx15=36ms^-1#

#t_2-> "duration of second phase journey"=200s#

This journey occurs at constant velocity #v_2#

So distance traversed in this phase

#s_2=v_2xxt_2=36xx200=7200m#

For third phase journey

#v_2->"initial velocity"=36ms^-1#

#a_2->"uniform acceleration in 3rd phase"=-3.6ms^-2#

#v_3-> "Final velocity of the car "=0#

#t_3->"duration of 3rd phase journey"=?#

So #v_3=v_2+a_2xxt_3#

#=>0=36+(-3.6)xxt_3#

#=>t_3=10s#

Distance traversed in 3rd phase

#s_3=1/2(v_2+v_3)xxt_3#

#=>s_3=1/2(36+0)xx10=180m#

So total duration #" "T=t_1+t_2+t_3=15+200+10=225s#

Total distance traversed

#S=(s_1+s_2+s_3)=(270+7200+180)m=7650m#

So average speed #V_"av"=S/T=7650/225ms^-1=34ms^-1#

Feb 4, 2017

Answer:

#"A different approach"#

Explanation:

enter image source here

#"------------------------------------------------"#

#"use triangle OAE(for phase 1)"#

#tan alpha="acceleration"#

#2.40=v/15#

#v=36 " m/s"#

#"area=distance covered"#

#"area="(36*15)/2=270" meters"#

#"-----------------------------------------------"#

#"use rectangle ABFE(for phase 2)"#

#"area=distance covered for interval t=15 and t=215"#

#"area="200*36=7200" meters"#

#"-----------------------------------------------"#

#"use triangle BFC(for phase 3)"#

#tan beta="deceleration"#

#3.6=36/k#

#k=36/3.6=10#

#t=10+215=225" s"#

#"area=distance covered for interval t=215 and t=225"#

#area=(36*10)/2=360/2=180" meters"#

#"time elapsed="15+200+10=225 " seconds"#

#"total distance covered="270+7200+180=7650" meters"#

#"average speed=" ("total distance covered")/("elapsed time")#

#"average speed="7650/225=34" m/s"#