Question

The position versus time for a certain object

Answer 1

Answer:

$\dfrac{dx}{dt}=3\ m/s$

Explanation:

The given graph shows the position versus time for a certain object  moving along the x-axis. We need to find the instantaneous velocity at 1 s. We know that the slope of position time graph gives the velocity and for a particular instant known as instantaneous velocity. Mathematically,

$v=\dfrac{dx}{dt}$

Taking slope of the given graph as :

At 1 s the position of the object is, $x_2=4\ (approx)$ and $x_1=1$

$\dfrac{dx}{dt}=\dfrac{x_2-x_1}{t_2-t_1}$

$\dfrac{dx}{dt}=\dfrac{1-4}{0-1}$

$\dfrac{dx}{dt}=3\ m/s$

So, the instantaneous velocity at 1 s is 3 m/s. Hence, this is the required solution.

Answer 2

To find instantaneous velocity given a position vs. time graph is find the derivative at that given point. In other words, find the slope at that point.

So at t = 1s, the velocity is 5/2 m/s.

Hope this helps!