Question

The acceleration at any instant is the slope of the tangent of the ___________ curve at that instant.

Answer 1

Acceleration:

1. Acceleration is defined as the rate of change of velocity with respect to time.
2. Mathematically, it is expressed as $a=\frac{dv}{dt}\dots \left(1\right)$.

Velocity-time graph

Velocity-time graph:

1. The slope of a line is found by $\tan \theta$.
2. The value of tangent of an angle is the ratio of perpendicular and base.
3. Thus, from the figure it is clear that $slope=\tan \theta =\frac{dv}{dt}\dots \left(2\right)$

From equation $\left(1\right)$ and equation $\left(2\right)$, it is clear that slope of velocity-time graph gives acceleration.

Hence, the acceleration at any instant is the slope of the tangent of the velocity-time curve at that instant.