Acceleration-time graph

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Acceleration-time graph

From the acceleration-time plot of a moving particle, we can deduce the following information.

• We can have average acceleration for the anytime interval from the given acceleration-time plot.
• We can find change in velocity for given time interval from acceleration-time plot by using the expression,
• dv = a dt i.e.,

velocity-time graph from the given a-t plot. Information about the initial velocity has to be mentioned explicitly. Once we have a v-t plot we can have all the information as discussed in the previous graph.

If acceleration is constant, then velocity-time plot would be a straight line.

Velocity-displacement graph

This graph is not very common but very conceptual questions can be framed on the basis of the graph. The following points you keep in mind while dealing with this graph.

once you have the slope of the tangent drawn to the v-x curve you can have acceleration at any instant, and from this information you can also see whether the particle is accelerating or decelerating.

Classification of Rectilinear Motion

As such in general classication of rectilinear motion is not done, but for the sake of your convenience we are classifying it as follows:

1. Uniform motion i.e., velocity is constant and acceleration is zero.

2. Uniformly accelerated motion, in this acceleration, is constant.

3. Non-uniformly accelerated motion, in this acceleration, varies.

Uniform Motion

The salient features of this motion are:

• Velocity is constant.
• Acceleration is zero.
• For any time interval, distance and displacement are the same.
• Average velocity, average speed, instantaneous speed and velocity are all having the same value.
• The direction of motion is not changing.

Uniformly Accelerated Motion

Here acceleration is constant i.e., uniform and the motion of the particle is non-uniform. If initial velocity and acceleration are in the same direction, the particle’s speed increases continuously as time passes and distance and displacement would be always equal. If the initial velocity and acceleration are in opposite direction then particle decelerates for some time and then accelerates in opposite direction, i.e., the direction of motion changes at the instant when velocity gets to zero. The equations of motion for a particle moving with a constant acceleration

Out of three equations of motion, the first two are vectors and the third one is scalar.

gives displacement and not distance.

The equation of motion is valid only when acceleration is constant.

Non-Uniformly Accelerated Motion