Can anyone confirm the answer I have to this question?

Question

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

Julia Aguilar · Accepted Answer

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#

Charlotte Aaron · Answer

#"A different approach"#

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

#"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"#

Adrian Ayala · Answer

undefined Sure, feel free to provide the answer to the question, and I'll do my best to confirm its accuracy for you.

Can anyone confirm the answer I have to this question?

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

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