Question

Can anyone confirm the answer I have to this question?

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

Answer 1

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`

Answer 2

`"A different approach"`

Explanation:

`"------------------------------------------------"`

`"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"`