Considering the movement of a body, speak about its coordinates, speed, acceleration. Each of these parameters has the formula of dependence on time if, of course, the speech not about the chaotic movement.
Instruction
1. Let the body move rectilinearly and evenly. Then its speed is presented by a constant, does not change over time: v = const. The formula of speed has an appearance of v=v (const) where v(const) is concrete value.
2. Let the body move ravnoperemenno (uniformly accelerated or ravnozamedlenno). As a rule, speak only about the uniformly accelerated movement, just in ravnozamedlenny the acceleration is negative. Acceleration is designated usually by letter a. Then speed is expressed by linear dependence on time: v=v0+a · t where v0 is initial speed, an is acceleration, t is time.
3. If to draw the schedule of dependence of speed from time, it will be a straight line. Acceleration – an inclination tangent of angle. At positive acceleration the speed grows and the straight line of speed directs up. At negative acceleration the speed falls and as a result reaches a zero mark. Further, with the same value and the direction of acceleration, the body can move only in the opposite direction.
4. Let the body move on a circle from a constant on the module speed. In this case it possesses the centripetal acceleration of a(c) directed to the center of a circle. It is called also normal acceleration of a(n). Linear speed and centripetal acceleration are connected by a=v ratio? / R where R is the radius of a circle on which the body moves.
5. For the movement on a curvilinear trajectory it is possible to determine still angular speed? and angular acceleration?. Linear speed, of course, is connected with angular by means of radius: v=? · R.
6. The formula of dependence of speed from time can have any appearance. By definition, speed is the first derivative of coordinate on time: v=dx/dt. Therefore if the dependence of coordinate on time of x=x (t) is set, the formula for speed can be found simple differentiation. For example, x (t) =5t? +2t-1. Then x' (t)= (5t? +2t-1)'. That is, v(t) =5t+2.
7. If further to differentiate a speed formula, it is possible to receive acceleration, acceleration – the first derivative of speed on time, and the second derivative of coordinate: a=dv/dt=d? x/dx?. But also speed can be received back from acceleration by integration. Only additional data will be necessary. Usually in tasks report entry conditions.