It is question about finding distance from velocity time graph?
3 Answers
See below.
Explanation:
If you have a graph of velocity against time, the area under the graph represents the distance.
This makes sense if you consider this:
On the graph:
Distance along t axis x distance along v axis.
You can find the area if it linear by using areas of squares, rectangles, trapeziums etc.
This is what I get
Explanation:
Let us start with Part
(ii) We need to use kinematic expression
#v=u+at#
Inserting given values
#V=-15+7.5xx(10-6)#
#=>V=-15+30=15\ ms^-1#
(iii)
- Area of trapezoid
#=1/2("sum of parallel bases")xx"height"#
Length of top base#=3.5-1.5=2\ s#
To calculate length of lower base we need to find time#t_1# when velocity becomes#=0# . Counting time from#t=3.5\ s#
From the information given in (i)#0=10+(-10)xxt_1#
#=>t_1=1\ s#
#:.# Length of lower base#=3.5+1=4.5\ s#
Now Area of trapezoid#=1/2(2+4.5)xx10=32.5\ m# - Area of first triangle
#=1/2"base"xx"height"#
To calculate length of base we need to find time#t_2# when velocity becomes#=0# . Counting time from#t=6\ s#
From the information given in (ii)#0=-15+7.5xxt_2#
#=>t_2=2\ s#
#:.# Length of base#=# Time gap between two instances when velocity becomes zero#=8-4.5=3.5\ s#
Area of first triangle#=1/2xx3.5xx|-15|=26.25\ m#
We have taken the magnitude of velocity as we need to find distance which is a scalar quantity.
(if we take negative sign in consideration we will get displacement which is a vector quantity) - From the given and calculated values
Total distance#=100=# Area of trapezoid#+# Area of first triangle#+# Area of second triangle
#=>100=32.5+26.25+# Area of second triangle
#=># Area of second triangle#=41.25\ m#
#41.25=1/2"base"xx"height"#
#=>41.25=1/2"base"xx15#
#=>"base"=41.25xx2/15=5.5\ s#
#:.T=8+5.5=13.5\ s#
Explanation:
For question (ii), you have made an error.
Using
Initial velocity
Acceleration
Question (iii).
We need to find areas A , B, C
In order to do this we first need to find
For
From question (i) we are told acceleration between 3.5 and 6 is
Using
Velocity is zero at
Velocity is
For
We know from (ii), that the acceleration between
Velocity at
Velocity at
Using
Area of trapezium (trapezoid) A
Area of triangle B
Area of triangle C
The sum of these areas is
Solving for T: