When Will the Cars Collide? A Problem in Accelerated Linear Motion

In summary, two cars, A and B, are traveling at a constant velocity of 20 m/s on a straight road. Car A is 15m behind car B. When they reach point P, both cars decelerate at a rate of 4m/s^2. It can be shown that the cars will collide at the point where they stop, and this collision will occur at a distance from P. The motion of both cars can be represented on the same speed-time graph.
  • #1
mcintyre_ie
66
0
If anybody could offer any help with this id be eternally gratefull

Two cars A and B, each 5m in length, travel with constant velocity 20 m/s along a straight level road. The front of car A is 15m directly behind the rear of car B. Immediately on reaching a point P, each car decelerates at 4m/s^2.
1) Show that A collides with B
2) At what distance from P does the collision occur?
3) Show the motion of both cars on the same speed-time graph.

Thanks in advance
 
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  • #2
The cars will collide at the point where they stop (B stops first and A stops at the same point). I'll leave the rest as an exercise in elementary calculus.
 

1. What is Accelerated Linear Motion?

Accelerated linear motion is the motion of an object in a straight line with a changing velocity. This means that the object is either speeding up or slowing down as it moves.

2. How is Accelerated Linear Motion different from Constant Linear Motion?

Constant linear motion is when an object moves in a straight line with a constant velocity, meaning it does not speed up or slow down. Accelerated linear motion, on the other hand, involves a changing velocity and can be caused by a force acting on the object.

3. What causes Accelerated Linear Motion?

There are several factors that can cause accelerated linear motion, including a force acting on the object, a change in direction, or a change in the mass of the object.

4. How is Accelerated Linear Motion measured?

The rate of acceleration in linear motion can be measured using the equation a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval.

5. What real-life examples demonstrate Accelerated Linear Motion?

Some examples of accelerated linear motion in everyday life include a car accelerating from a stop, a roller coaster going down a steep hill, and a ball rolling down a hill. These all involve a change in velocity and are therefore considered accelerated linear motion.

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