The time taken by the automobile to overtake the truck is t=6seconds.
The motion of the automobile and the truck can be analyzed using the kinematic equations of motion. Let's denote the distance covered by each vehicle as s and the time taken as t. The kinematic equation relates these variables as s=ut+ 1/2 at^2, where u is the initial velocity, a is the acceleration, and t is the time.
For the truck:
s truck = 1/2⋅2.1⋅t^2truck
For the automobile:
s auto = 1/2⋅3.4⋅t^2 auto
Given that the truck has moved 40 meters when the automobile overtakes it, we can set up an equation:
40= 1/2.2.1⋅t^2 truck
Solving for t truck gives t =4 seconds.
Now, since the automobile overtakes the truck, we can set up another equation for the distance covered by the automobile: s auto=3.4⋅t^2 auto
Given that the automobile overtakes the truck after the truck has moved 40 meters, we substitute t auto =t truck+t overtake and s auto=40+s truck. Solving for t overtake yields t overtake=6 seconds. Therefore, the automobile takes 6 seconds to overtake the truck.