Question

How do you calculate instantaneous velocity from a position-time graph or an acceleration-time graph?

Answer 1

To calculate the instantaneous velocity from a position-time graph or an acceleration-time graph, you can use calculus.

1. Position-Time Graph: To find the instantaneous velocity from a position-time graph, you need to calculate the derivative of the position function with respect to time. The derivative of the position function represents the rate of change of position, which is the velocity.

Let's denote the position function as $s(t)$, where $s$ represents position and $t$ represents time. The derivative of $s(t)$ with respect to $t$ gives us the instantaneous velocity function $v(t)$:

$v(t)=\frac{ds(t)}{dt}$

For example, if the position function is given as $s(t)=3t^2+2t+1$, we can differentiate it with respect to $t$ to obtain the instantaneous velocity function $v(t)$:

v(t)=ddt(3t2+2t+1)=6t+2v(t) = frac{d}{dt}(3t^2 + 2t + 1) = 6t + 2v(t)=dtd​(3t2+<span class="strut" style="height: 0.7278em; vertica