Question

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.5 m/s2. At the same instant a truck, traveling with a constant speed of 8.7 m/s, overtakes and passes the automobile?

Answer 1

6.96 s

Step-by-step explanation:

Given:

• u = initial speed of the automobile = 0 m/s

• a = constant acceleration of the automobile =
  `2.5\ m/s^2`
• v = constant speed of the truck = 8.7 m/s

Assume:

• t = time instant at which the automobile overtakes the truck.

At the moment the automobile and the truck both meat each other the distance travel by both vehicles must be the same.

`\therefore \textrm{Distance traveled by the automobile }=\textrm{Distance traveled by the truck}\\\Rightarrow ut+(1)/(2)at^2=vt\\\Rightarrow (0)t+(1)/(2)* 2.5* t^2=8.7t\\\Rightarrow 1.25t^2=8.7t\\\Rightarrow 1.25t^2-8.7t=0\\\Rightarrow t(1.25t-8.7)=0\\\Rightarrow t = 0\,\,\,or\,\,\, t = (8.7)/(1.25)\\\Rightarrow t = 0\,\,\,or\,\,\, t = 6.96\\`

Since t = 0 s is the initial condition. So, they both meet again at t = 6.96 s such that the automobile overtakes the truck.