Catch/Overtake Problems Practice Problems

A runner is at rest at the start line of an athletic field and is passed by his trainer, who is moving at a constant speed of 4.5 m/s on his bike. When his trainer passes the start line, the runner begins to accelerate, increasing his speed by applying a constant acceleration of 0.75 m/s². Determine the speed of the runner when he catches his trainer.

A police officer at rest on a sidewalk is passed by a thief running at a steady speed of 3.50 m/s. Just as the thief exceeds him, the police officer accelerates at a rate of 1.00 m/s². Determine the distance the police officer travels before catching the thief.

A van of Swift (a company that delivers packages) was initially parked at Cornelia Street. Then, it starts moving with an acceleration of 3.2 m/s². At the instant it has started moving, a van of its competitor, Thunder, traveling with a constant speed of 22.0 m/s, overtakes and passes the van of Swift. What is the speed of the van of Swift when it overtakes the van of Thunder?

A van of Swift (a company that delivers packages) was initially parked at Cornelia Street. Then, it starts moving with an acceleration of 3.2 m/s². At the instant it has started moving, a van of its competitor, Thunder, traveling with a constant speed of 22.0 m/s, overtakes and passes the van of Swift. Determine the distance from the starting point that the van of Swift overtakes the van of Thunder.

Two cars A and B are moving directly towards each other in a straight line. Each car has a speed of 72 km/h. If they were initially 4.3 km apart, how long would it take for them to collide?

A young skater aims to catch up with his friend, who is skateboarding at a constant speed of 3.8 m/s. Starting from rest, the young skater accelerates at 1.1 m/s² until reaching his maximum speed of 4.8 m/s, which he maintains thereafter. Calculate the distance the young skater has traveled by the time he catches up to his friend. Note that the two friends start skating from the same point.

The figure below illustrates the position vs time plot for two bikes, P and Q. At what specific time(s) do the bikes cross paths? Which bike overtakes the other?

The position vs time graph for two snowmobiles P and Q is shown in the figure below. Determine which snowmobile exhibits a greater average velocity.

Car P and Car Q are moving towards a cabin. They both have different speeds. When Car P is 98 m from the cabin, it is cruising at 45 m/s and is 22 m behind Car Q, which has a speed of 55 m/s. Due to a mechanical issue, Car Q decelerates at a constant rate of 3.2 m/s² for the rest of the way. Determine the constant acceleration that car P needs to maintain to tie (finish side-by-side) with car Q right at the end.

A compressed spring fires vertically a small ball from the floor with an initial speed of 6.00 m/s. Simultaneously a student located exactly at a distance d above the spring releases a box without an initial speed. Determine the position of the student above the floor at which the ball is at its maximum elevation when it strikes the box.

Two friends riding their respective bikes meet at a traffic signal and race to the next signal 600 m away. One friend is riding a red bike while the other is on a black bike. The red bike starts ahead of the black bike by 2.0 s. The acceleration of the red bike is 4.5 m/s² which is smaller than the black bike's acceleration of 5.5 m/s². Determine who will reach the traffic light first.

A train leaves a station terminal with a constant acceleration of 2.0 m/s². A late traveler 5.0 m behind the entry of the train runs at a constant speed of 5 m/s trying to access the train. How long can the traveler wait before beginning to pursue and still make it to the train?

An experiment consists of releasing a metallic sphere from rest from the top of a vertical tube of length l, and at the same instant, a popgun located at the bottom of the tube fires a ping-pong ball at a speed of 5 m/s. Determine the greatest length the tube can have in order for the collision to take place before the ping pong ball hits the bottom of the tube.

The following training was conducted to evaluate the police officers' performance during a thief arrest.  A police officer notices a thief robbing a car. The police officer runs in the direction of the thief, attaining a constant speed of 6.5 m/s. Unfortunately, the police officer can only maintain this maximum speed for 25 seconds before having to stop. The instant the police officer is at his maximum speed, the thief is warned. At this instant, the police officer and the thief are 75 meters apart. The thief starts to run, accelerating at a constant rate of 2 m/s² for 3 s, and then he maintains his speed. Does the thief end up in jail? If not, how far ahead is the thief when the police officer stops?

A box is released from rest from a balcony. At the same instant, a worker standing below the balcony throws a ball vertically with an initial speed of 8.00 m/s. The distance separating the hands of the worker and the balcony is 10.0 m. Determine the position, with respect to the hand of the worker, where the ball and the box meet.