Editing Content :: Admin Scraper

Chapter

Content type

Position

Value

16 PHYSICS Instantaneous acceleration is defined in the (c) An object is moving in negative direction same way as the instantaneous velocity : with a negative acceleration. (d) An object is moving in positive direction a = lim v = dv (2.3) till time t and then turns back with the t 0 t dt 1 The acceleration at an instant is the slope same negative acceleration. An interesting feature of a velocity-time of the tangent to the v–t curve at that instant. graph for any moving object is that the area Since velocity is a quantity having both under the curve represents the displacement over a given time interval. A magnitude and direction, a change in velocity may involve either or both of these general proof of this statement requires use of factors. Acceleration, therefore, may result calculus. We can, however, see that it is true from a change in speed (magnitude), a for the simple case of an object moving with change in direction or changes in both. Like constant velocity u. Its velocity-time graph is velocity, acceleration can also be positive, as shown in Fig. 2.4. negative or zero. Position-time graphs for motion with positive, negative and zero acceleration are shown in Figs. 2.4 (a), (b) and (c), respectively. Note that the graph curves upward for positive acceleration; downward for negative acceleration and it is a straight line for zero acceleration. Although acceleration can vary with time, our study in this chapter will be restricted to motion with constant acceleration. In this case, the average acceleration equals the constant value of acceleration during the interval. If the velocity of an object is voat t = 0 and v at time t, we have v −v 0 a = t − 0 or, v = v0+ at (2.4) Fig. 2.3 Velocity–time graph for motions with Fig. 2.2 Position-time graph for motion with (a) positive acceleration; (b) negative constantacceleration.(a)Motioninpositive acceleration, and (c) zero acceleration. direction with positive acceleration, (b) Motion in positive direction with Let us see how velocity-time graph looks like negative acceleration, (c) Motion in negative direction with negative for some simple cases. Fig. 2.3 shows velocity- time graph for motion with constant acceleration acceleration, (d) Motion of an object with for the following cases : negative acceleration that changes direction at time1t . Between times 0 to (a) An object is moving in a positive direction t , it moves in positive x - direction with a positive acceleration. and between t and t it moves in the (b) An object is moving in positive direction 1 2 opposite direction. with a negative acceleration. Reprint 2026-27