A car accelerates from rest with `a =2 m//sec^(2)` in a straight track, then it comes to rest applying its brakes after a time T 20 seconds covering a distance of 100 m. Using a graphical method, find the maximum speed of the car..

Explanation

To solve the problem step by step, we will analyze the motion of the car using a velocity-time (v-t) graph.

### Step 1: Understanding the Motion
The car starts from rest (initial velocity \( u = 0 \)) and accelerates with an acceleration \( a = 2 \, \text{m/s}^2 \) for a certain time \( T_1 \), then it decelerates to rest over the remaining time \( T_2 \). The total time for the entire motion is given as \( T = 20 \, \text{s} \).

### Step 2: Finding the Maximum Speed
During the acceleration phase, we can calculate the maximum speed \( V_0 \) reached by the car at the end of the acceleration phase. The formula for final velocity when starting from rest under constant acceleration is:
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