Question

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

Answer 1

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

$a = \frac{v - u}{5}$

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,
$v - u = a \times t$

This the final derivation from the above given condition.

Answer 2

Answer:

This is the answer up.....Hope it helps