Physics/motion in straight line
QUESTION: the displacement of a body is given by s=1/2gtsquare, where g is acceleration due to gravity. the velocity of the body at any time t is ?
ANSWER: Hello saroj,
Notice the changes I have made in your first sentence. The displacement of a falling body (ignoring air resistance) is given by s=(1/2)*g*t^2, where g is acceleration due to gravity and the body has initial velocity of zero.
OK, so that says that in time t, it travels a distance of s. So that means that the average velocity during time t, is given by
Vave = s/t = (1/2)*g*t^2 / t = (1/2)*g*t
Since the body started with Vi = 0, the velocity during the first half of the time is less than the average and the velocity during the second half of the time is more that the average. In fact, at the moment when the time is 1/2 of the total time, the velocity has increased from zero to (1/2)*g*t. And during the second half of the total time, the speed increases from (1/2)*g*t to 2X as large a speed. In the second half of the total time, the body again increases speed by (1/2)*g*t over what it was at the start of the time period.
So during the fall, the initial speed increases from Vi and at the end of the fall the speed is Vf where
Vi = 0
Vf = (1/2)*g*t + (1/2)*g*t= g*t
Because the acceleration is constant throughout the fall, to find the average speed, you can do a simple arithmetical average calculation:
Vave = (0 + g*t^2) / 2
Look up 2 paragraphs and study the last line.
Vf = g*t
So if you start with zero velocity, for any time t the current velocity is g*t.
I hope this helps,
---------- FOLLOW-UP ----------
QUESTION: a man moves in a open field such that after moving 10 m on a straight line, he makes a sharp turn of 60 degree to his left . the total displacement after 8 such turns is equal to?
Hello again saroj,
The interior angles of an equilateral triangle are all 60 degrees. Therefore he is walking along the sides of an equilateral triangle. After 3 such turns, his displacement is zero. After 6 such turns his displacement is zero. After 2 more such turns he has only the last side of the triangle to walk along to return to the starting point. So after that 8th turn he is 10 m from the start.
I hope this helps,