Solved step by step with explanation - Graphs: s-t, v-t and accelerations

Question

Solved step by step with explanation - Graphs: s-t, v-t and accelerations

Step 1: Understanding the Given Information

We have a material point moving in the s-direction (presumably along a straight line). The given information is as follows:

We can use the kinematic equation for displacement to find the acceleration:

\[ s = ut + \frac{1}{2} a t^2 \]

- \( t \) is the time

Since the displacement is zero at t=10 seconds and the initial displacement is 2 meters:

Step 3: Finding Acceleration (a) at t=6 seconds

Since we know the displacement at t=6 seconds is not provided, we cannot directly use the displacement equation. However, we can relate acceleration and speed using the following equation:

Since \( u \) (initial velocity) is zero at t=6 seconds:

\[ 0 = -2 \cdot a \cdot s \]

1. Displacement-Time Graph (\( s-t \)):

- On the horizontal axis (time axis), plot time (\( t \)).

- On the horizontal axis (time axis), plot time (\( t \)).

- On the vertical axis (velocity axis), plot velocity (\( v \)).

- Acceleration at t=6 seconds: \( 0 \, \text{m/s}^2 \)

You can use these results to create the graphs as described in step 4.