Question

Question #f0ab4

Answer 1

`"The velocity of object at the midpoint is v = "5sqrt(5)" "m/s`

Explanation:

• Please examine the chart carefully.The graph is not drawn in scale.
• The gradient of the velocity-time graph gives the acceleration of the motion.

`"given : "a=5" " m*s^(-2)`

• let us calculate the slope of the D C E triangle.

`5=(|CE|)/(|DE|)=tan theta`

`CE=15-5=10`

`DE=t-0=t`

`5=10/t`

`t=10/5`

`t=2" seconds"`

-We calculate the area colored in green to find the displacement of the motion.

`"area=displacement"=Delta x=(15+5)/2*t`

`"Substitute t=2"`

`"area=displacement="Delta x=20/cancel(2)*cancel(2)`

`Delta x=20" "meters.(" distance from A to B")`

`"Midpoint of AB is 10 meters."`

• We can calculate the midpoint velocity of the motion using the fallowing formula.

`v^2=v_i^2+2*a*Delta x`

`v_i=5 m/(s)`

`v=?" (midpoint velocity)"`

`a=5" "m/s^(2)`

`Delta x=10 m`

`v^2=5^2+2*5*10`

`v^2=25+100`

`v^2=125`

`"let us take square root the both sides of equation."`

`sqrt v^2=sqrt(125)`

`v=5sqrt(5)" " m/s`