Question

To derive the first equation of motion, which graph is more helpful?

• A. Distance-time graph
• B. Displacement-time graph
• C. Velocity-time graph
• D. Speed-time graph

Answer 1

The correct option is C Velocity-time graph

First equation of motion is $v=u+at$.
Where v is final velocity, u is initial velocity, a is acceleration and t is time period.
To derive this equation, velocity-time graph is more suitable than any other graph. The main reason is the slope of velocity-time graph gives acceleration. Since we need acceleration which we get using change in velocity per unit time.

From the graph it is clear that, the slope of a velocity line is $\frac{v-u}{t}$ which is acceleration a.
After rearranging the terms we get,
v = u + at (1st equation of motion)