Answer to Question #161105 in Mechanics | Relativity for Hamza Khurshid

Question

A lorry of length 16m is travelling at a constant speed of 12ms^-1 in the inside lane of a straight road.

A car of length 4m is initially travelling in the outside lane in the same direction as the lorry and at the same speed. The gap between the two vehicles is 50m.

The car accelerates at 2ms^-2 for 5 seconds, then travels at constant speed for a time and finally decelerates at 2ms^-2 for 5 seconds. Now the car is travelling at the same speed as before, but in front of the lorry and the gap is the same as it was before.

How long did the car take to get from its initial position to its final position?

How far did the car travel in this time?

I will try to draw a diagram, hopefully it comes out good:

initial positions:

car-------------space in between--------Lorry

|---|----------------------------------------|----------|

4m----------50m--------------------------16m

Final positions

Lorry-------space in between--------car

|------------|------------------------------|---|

16m----------50m----------------------4m

Answer 1

First distance is 50+16=66 m, last distance is 50+4=54 m.

$v_1=v+at=12+10=22~\frac ms.$

$s_1=\frac{at^2}{2}=25~m=s_2.$

$s=(66-25)+(54-25)=70~m.$

Total time is $t_{total}=5+\frac{s}{v_1-v}+5=17~s.$

Total distance is $s_{total}=66+54=120~m.$