Acceleration and Velocity

Galileo concluded that the rate of change of velocity with time is a constant of motion for all objects in free fall.

Instantaneous acceleration is defined as the slope of the tangent to the v-t curve at a specific instant.

The acceleration-time curve represents how acceleration changes over time.

<p>Acceleration is considered uniform when it has a constant value over a specific time interval.</p> Signup and view all the answers

<p>When acceleration is uniform, it equals the average acceleration over that period.</p> Signup and view all the answers

<p>Galileo found that the change in velocity with distance is not constant; it decreases with increasing distance of fall.</p> Signup and view all the answers

<p>Velocity is a quantity with both magnitude and direction, while acceleration can result from a change in speed, a change in direction, or changes in both.</p> Signup and view all the answers

<p>The graph curves upward for positive acceleration, downward for negative acceleration, and is a straight line for zero acceleration.</p> Signup and view all the answers

<p>Acceleration is constant when its value remains the same during the motion interval.</p> Signup and view all the answers

<p>The equation is $v=v_0 + a(t-0)$ or $a = rac{v-v_0}{t-0}$.</p> Signup and view all the answers

<p>An example is the motion of the car in Fig 3.3 between $t=18s$ and $t=20s$.</p> Signup and view all the answers

<p>An example is the motion of a car moving from O in Fig. 3.1 in the negative x-direction with increasing speed.</p> Signup and view all the answers

<p>Instantaneous acceleration is defined as the limit of the average acceleration as the time interval approaches zero.</p> Signup and view all the answers

<p>The acceleration of an object at a particular time is the slope of the velocity-time graph at that instant of time.</p> Signup and view all the answers

<p>The area under the velocity-time curve between times t1 and t2 is equal to the displacement of the object during that interval of time.</p> Signup and view all the answers

<p>In uniformly accelerated rectilinear motion, displacement x, time taken t, initial velocity v0, final velocity v, and acceleration a are related by kinematic equations: v = v0 + at, x = v0t + 1/2at^2, v^2 = 2v0^2 + 2ax.</p> Signup and view all the answers

<p>The displacement depends only on the end points, while the path length depends on the actual path taken.</p> Signup and view all the answers

<p>For uniform motion, x-t graph is a straight line inclined to the time axis, and the v-t graph is a straight line parallel to the time axis. For motion with uniform acceleration, x-t graph is a parabola, and the v-t graph is a straight line inclined to the time axis.</p> Signup and view all the answers