Question

Name the two quantities , the slope of whose graph gives speed and acceleration

Answer 1

Answer:  

The two quantities are distance and velocity with respect to time.

Solution:

The speed is defined as the rate of change of distance per unit time. So, it is ‘equal to the slope’ of the distance vs. time graph. Mathematically it can be proved.  

First consider the mathematical representation of speed as,

$\bold{\text { Speed }=\frac{\text { Distance }}{\text { Time }} \rightarrow(1)}$

Second, in a distance vs time graph where distance is in y axis and time is in x axis, the slope is

$\bold{\text { Slope }=\frac{y-\text { axis }}{x-\text { axis }}=\frac{\text { Distance }}{\text { Time }} \rightarrow(2)}$

From (1) and (2), it can proved mathematically that slope of ‘distance’ versus ‘time graph’ will be equal to the speed.

Similarly, the acceleration is defined as the ‘rate of change of velocity’ per unit time. So it will be equal to the slope of velocity vs time graph. ‘Mathematically’ it can be proved as above.

First consider the mathematical representation of acceleration as,

$\bold{\text { Acceleration }=\frac{\text { Velocity }}{\text { Time }} \rightarrow(3)}$

Second, in a velocity vs time graph where velocity is in y axis and time is in x axis, the slope is  

$\bold{\text { Slope }=\frac{y-\text { axis }}{x-\text { axis }}=\frac{\text { Velocity }}{\text { Time }} \rightarrow(4)}$

From (3) and (4), it can proved mathematically that slope of velocity vs time graph will be equal to the acceleration.

Answer 2

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