Question

Draw a graph for acceleration against time for uniformly accelerated motion. How can it be used to find the change in speed in a certain interval of time.

Answer 1

Here is your answer

The graph (sample) is in the attachment

Let the vertical line represent the Acceleration and the horizontal line represent the time

O is the origin

There is positive Acceleration from O to A and Acceleration is constant from A to B

Also, there is deceleration from B to E

Now,

Let the time intervals be constant.

O to C = 5 sec

C to D = 5 sec

D to E = 5 sec

Also at O the initial velocity is o m/sec

From this (situation from O to C)

Now,

From O to C :-

Time = 5 seconds

Initial velocity = u m/sec

Final velocity = v m/sec

So,

a = v - u / time between O to C

So, in this situation

Next situation :-

From D to E

Time is 5 sec

Initial velocity = u m/sec

Final velocity = v m/sec

But,

Since there is deceleration, u will be greater than v

So,

A= v-u/5

So,

From this 5a = v-u

V-u is the change in the velocity.

From the above two situations

Change in velocity = Acceleration * time

So,

This the final derivation from the above given condition

Answer 2

Answer:

Your answer is in the ATTACHMENT