Problem: At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s2. At the same instant a truck, traveling with a constant speed of 9.5 m/s, overtakes and passes the automobile.(a) How far beyond the traffic signal will the automobile overtake the truck?(b) How fast will the automobile be traveling at that instant?

FREE Expert Solution

In this problem, we're asked to determine displacement and final speed at the time when the two objects meet.  

This is a problem about one object catching up to another (“meet and catch” type problem). 

To solve meet-and-catch type problems, we’ll always organize what we know about the problem, then follow these steps:

  1. Write the position equation for each object using UAM equation (3).
  2. Set the position equations equal to each other.
  3. Solve for time.
  4. (If needed) Plug the time back into another equation to solve for x or v.

Since we’re not given information about gravity acting on either of them, we can assume they’re both traveling horizontally. We’re also given that they both have constant acceleration (in this case, one of the accelerations is zero), meaning we can use the UAM equations. Recall that the four UAM equations are:

 (1)  vf = v0 +at (2) x=(vf+v02)t (3) x=v0t+12at2 (4)  vf2=v02 +2ax 

In this problem, we’re directly given two pieces of information: the constant acceleration of the automobile, aA = 2.2 m/s2, and the constant velocity of the truck, vT = 9.5 m/s.

There's also some information that the problem implies: that the truck and auto are both at = 0 at the instant the traffic light turns green (which we’ll say is = 0); the auto starts moving at that instant, so its initial velocity v0A = 0; the truck is moving at a constant velocity, so aT = 0. 

Let's organize our target, known, and unknown variables for the two vehicles:

For the truck:
i. a = aT = 0
ii. v0 = vf = vT = 9.5 m/s
iii. x0 = 0
iv. xf = xT = ?
v. t = ?

For the car:
i. a = aA = 2.2 m/s2
ii. v0 =  v0A = 0
iii. vf =  vfA = ?
iv. x0 = 0
v. xf = xA = ?
vi. t = ?

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Problem Details

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.2 m/s2. At the same instant a truck, traveling with a constant speed of 9.5 m/s, overtakes and passes the automobile.

(a) How far beyond the traffic signal will the automobile overtake the truck?

(b) How fast will the automobile be traveling at that instant?