Derive the equations v = u + at, s = ut + ½at2 and v2 = u2 + 2as graphically.
2. What is uniform circular motion ? Give two examples which force is responsible for that.
3.What can you say about the motion of a body if its displacement-time graph and velocity-time graph both are straight line ?
Answers
Answer:
what you are writing
Explanation:
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Explanation:
Graphical Derivation of First Equation
Consider an object moving with a uniform velocity u in a straight line. Let it be given a uniform acceleration a at time t = 0 when its initial velocity is u. As a result of the acceleration, its velocity increases to v (final velocity) in time t and S is the distance covered by the object in time t.
The figure shows the velocity-time graph of the motion of the object.
Slope of the v - t graph gives the acceleration of the moving object.
Thus, acceleration = slope = AB =
v - u = at
v = u + at I equation of motion
Graphical Derivation of Second Equation
Distance travelled S = area of the trapezium ABDO
= area of rectangle ACDO + area of DABC
(v = u + at I eqn of motion; v - u = at)
Graphical Derivation of Third Equation
S = area of the trapezium OABD.
Substituting the value of t in equation (1) we get,
2aS = (v + u) (v - u)
(v + u)(v - u) = 2aS [using the identity a2 - b2 = (a+b) (a-b)]
v2 - u2 = 2aS III Equation of Motion
2). The final motion characteristic for an object undergoing uniform circular motion is the net force. The net force acting upon such an object is directed towards the center of the circle. The net force is said to be an inward or centripetal force.
3) If displacement-time graph is a straight line inclined to the time axis at an acute angle, it means that gradient of the curve or velocity of the body is non-zero. Therefore, body is moving away from the starting point with uniform velocity.
