![]() ![]() Let us consider a body moving with uniform acceleration ‘a’ having initial velocity ‘u’ attains the final velocity v in time ‘t’ covering a distance ‘s’ as shown in the graph. GRAPHICAL DERIVATION OF EQUATIONS OF MOTION For this small time interval, distance ΔS = vΔt = Area of the blackened strip.įor whole time-interval between t 1 and t 2ĭistance = sum of area of all the strips between t 1 and t 2 = Area of shaded figure PQRS. Over a small interval of time, the speed can be taken as constant. Hence distance = PQ × SP = Area of rectangle PSRQĬase (ii) : When speed (velocity) as well as acceleration is non-uniform (variable)įigure shows the speed- time graph of a body moving with variable speed and acceleration. Distance covered by this taxi from time t1 = 4h at P to time t2 = 8 h at S, is given by distance = 50 × (t 2 - t 1) It is a straight line parallel to X - axis (time axis). u = 20 m/s, a = - g = - 9.8 m/s2 (moving against gravity)ĭISTANCE (DISPLACEMENT) FROM SPEED (VELOCITY) TIME GRAPH:Ī distance (displacement = speed (velocity) x time, so the distance (displacement) can be calculated (computed) with speed (velocity) - time graph.Ĭase (i): When speed (velocity) is uniform (constant):įigure shows the speed - time graph of a car moving with a uniform speed of 50 km h-1. How high did the ball go? (take g = 9.8 m/s2.Īns. A ball is thrown vertically upwards with a velocity of 20 m/s. A car attains 54 km/h in 20 s after it starts. Calculate the acceleration of the car.Īns. Two seconds thereafter it is moving at 60 km/h. Initial velocity = +v 0 (in upward directions)ĭisplacement = –h (in downward direction) Let initial velocity is v 0 which is in vertically upward direction and finally comes down to the ground as shown in figure. Motional quantities, which are in downward-direction, are taken as negative. Motional quantities in upward-direction are taken as positive. To solve such types of problem, the following sign convention is used:. When an object is thrown in space in such a way that at first it goes up and then comes down. When an object is thrown in a downward direction (taking positive) in space with initial velocity v0.Īcceleration = +g (in downward direction) When an object is thrown in upward direction (taking positive) in space with initial velocity v0.Īcceleration = –g (in downward direction) In a real experiment air resistance cannot be neglected. When an object is thrown upward or downward, in both cases same acceleration ‘g’ will be experienced by the object, which acts in downward direction. Here acceleration will be acceleration due to gravity. So equations of motion for uniformly accelerated motion can be used which are Motion under gravity is a uniformly accelerated motion. Motion under gravity means an object is in motion in space under the force of gravity alone. Motion of body is called free fall if only force acting on it is gravity (i.e. If a body moves with uniform velocity, its acceleration is zero i.e. ![]() If a body comes to rest, its final velocity v = 0 or, if a body reached the highest point after being thrown upwards its final velocity v = 0 but has acceleration (acting). If a body starts from rest its initial velocity u = 0. If a body is dropped from a height then its initial velocity u = 0 but has acceleration (acting). ![]() The distance covered by the body in nth second will be. [distance covered by a body along a straight line in n second. S = ut + 1/2 at 2 is the distance covered by a body in t s. Putting this value of ‘t’ in equation …(i) Distance traveled = Average velocity × timeįrom the second equation of motion we have, The distance traveled by moving body in time ‘t’ is ‘S’ then the average velocity = (v + u)/2. Suppose a body has an initial velocity ‘u’ and uniform acceleration ‘a’ for time ‘t’ so that its final velocity becomes ‘v’. This equation is known as the first equation of motion. Suppose it is subjected to a uniform acceleration ‘a’ so that after time ‘t’ its final velocity becomes ‘v’. Third Equation of motion : v 2 - u 2 = 2asĬonsider a body having initial velocity ‘u’.Second Equation of motion : s = ut + 1/2at 2.These equations are called equations of motion. When the body is moving along a straight line with uniform acceleration, a relation can be established between velocity of the body, acceleration of the body and the distance travelled by the body in a specific time by a set of equations. ![]()
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