The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).

Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt), represented by the equation v = Δs/Δt. Speed (or rate, r) is a scalar quantity that measures the distance traveled (d) over the change in time (Δt), represented by the equation r = d/Δt.

The slope of a velocity graph represents the acceleration of the object. So, the value of the slope at a particular time represents the acceleration of the object at that instant.

The slope of the distance-time graph indicates speed. It is because the slope of a distance-time graph determines the speed of that body, so the steeper the slope greater will be the speed of the body.

Using the Slope Equation

1. Pick two points on the line and determine their coordinates.
2. Determine the difference in y-coordinates for these two points (rise).
3. Determine the difference in x-coordinates for these two points (run).
4. Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

In retarded motion the velocity time graph is a straight line with negative slope. Explanation: Negative acceleration is called retardation. If the velocity of a body is decreasing with respect to time, the acceleration is said to be negative.

How to calculate velocity – speed vs velocity

1. Change minutes into seconds (so that the final result would be in meters per second). 3 minutes = 3 * 60 = 180 seconds ,
2. Divide the distance by time: velocity = 500 / 180 = 2.77 m/s .

Final velocity (v) of an object equals initial velocity (u) of that object plus acceleration (a) of the object times the elapsed time (t) from u to v. Use standard gravity, a = 9.80665 m/s2, for equations involving the Earth’s gravitational force as the acceleration rate of an object.

Final velocity (v) squared equals initial velocity (u) squared plus two times acceleration (a) times displacement (s). v2=u2+2as. Solving for v, final velocity (v) equals the square root of initial velocity (u) squared plus two times acceleration (a) times displacement (s).

Definition of Equations of Motion The following are the three equation of motion: First Equation of Motion : v=u+at. Second Equation of Motion : s=ut+/frac{1}{2}at^2. Third Equation of Motion : v^2=u^2+2as.

• Equations of Motions.
• In case of uniform acceleration, there are three equations of motion which are also known as the laws of constant acceleration.
• v = u + at.
• s = ut + ½at²
• where, s = displacement; u = initial velocity; v = final velocity; a = acceleration; t = time of motion.
• Equations of Motion.
• v = u + at.

Hence, these equations are used to derive the components like displacement(s), velocity (initial and final), time(t) and acceleration(a). Therefore they can only be applied when acceleration is constant and motion is a straight line….The three equations are,

1. v = u + at.
2. v² = u² + 2as.
3. s = ut + ½at²

Distance is a scalar quantity that refers to “how much ground an object has covered” during its motion. Displacement is a vector quantity that refers to “how far out of place an object is”; it is the object’s overall change in position.

Isaac Newton’s

3) The equation for acceleration is (a) a = vf – vi / t (b) a = (vf – vi ) / t (c) a = ( vf + vi ) / t. 5) Uniformly accelerated motion means that the acceleration is (a) constant (b) zero (c) varying uniformly. 6) In constant velocity motion, the acceleration is (a) zero (b) a nonzero constant (c) distance over time.

Some uniform accelerated motion examples include a ball rolling down a slope, a skydiver jumping out of a plane, a ball dropped from the top of a ladder and a bicycle whose brakes have been engaged.

acceleration. and this kind of motion is called accelerated motion. A body has uniform acceleration if it travels in a straight line and its velocity increases by equal amount in equal intervals of time for example freely falling bodies, motion of ball rolling down the inclined plane etc.

v2=v20+2ax. Since the acceleration is uniform, there is no need to use calculus to derive these. The first follows immediately from the meaning of acceleration. Distance travelled is the area under a speed : time graph.