Question #f0ab4

1 Answer
Jul 1, 2017

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

Explanation:

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  • 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