In a half marathon (13.1 miles), one runner finishes with a speed of 6.5 miles/hour and another finishes with 10 miles/hour. How long does the faster runner have to wait at the finish line to see the slower runner cross? Explain your final answer in minutes.

1. A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 4.0 m/s. Three seconds later the bicyclist hops on his bike and begins to follow the friend with an initial speed of 10 m/s. Assume the bicyclist continues at a constant speed of 10 m/s until he catches the friend. a) Calculate the time it takes to catch his friend. b) How fast is he moving when he catches his friend? c) How far did he travel to catch his friend?

In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a maximum speed of 183.58 mi/h. The one‐way course was 5.00 mi long. Acceleration rates are often described by the time it takes to reach 60.0 mi/h from rest. If this time was 4.00 s, and Burt accelerated at this rate until he reached his maximum speed,   a. how long did it take Burt to complete the course? b. Sketch position vs time, velocity vs. time, and acceleration vs. time graphs for the race.

An athlete wants to run a 1500m race with an average velocity of 6.00 m/s. After running the first 500m, he notices that the time elapsed is 100 seconds. Panicking, he accelerates for “t” seconds at 0.2 m/seconds^2 and finishes the race at his new faster speed. He makes it just in time. How long did he accelerate for? (Use 5 significant figures in the answer)

A Porsche challenges a Honda to a 200 m race. Because the Porsche's acceleration of 3.5 m/s2  is larger than the Honda's 2.8 m/s2, the Honda gets a 1 s head start. Who wins? By how many seconds?

A cat is being chased by a dog. Both are running in a straight line at constant speeds. The cat has a head start of 3.8 m. The dog is running with a speed of 9.1 m/s and catches the cat after 6.6 s. How fast did the cat run? m/s

In this question we will work through the steps to solve this question: A bus is travelling along a straight road at 25 m/s (90 km/h) when the driver sees a deer on the road and slams on the breaks. This causes a constant deceleration (a negative acceleration) of k m/s2. It takes the bus 5 seconds to stop. How far does the bus travel before coming to a stop? Steps in solution: Let t= 0 at the moment the bus driver slams on the breaks. Let v (t) be the velocity of the bus at time t (measured in m/s). Let s (t) be the position of the bus at time t (measured in meters), and let's choose s (0) = 0. a) Find v (0) in m/s. [Select] b) What does "a constant deceleration (a negative acceleration) of k m/s2" mean? [Select] c) What does "It takes the bus 5 seconds to stop" mean? [Select] d) Use the information in parts (a)-(c) to find a value for k, and an expression for v (t) [Select] e) Use the information from (d) as well as s (0) = 0 to find an expression for s (t). [Select] f) What should…

In a 5000 m race, the athletes run 12(1)/(2) laps; each lap is 400 m. Kara runs the race at a constant pace and finishes in 17.5 min. Hannah runs the race in a blistering 15.3 min, so fast that she actually passes Kara during the race. How many laps has Hannah run when she passes Kara?

The 1992 world speed record for a bicycle (human-powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 s, at which he commented, “Cogito ergo zoom!” (I think, therefore I go fast!). In 2001, Sam Whittingham beat Huber’s record by 19.0 km/h. What was Whittingham’s time through the 200 m?

A black mamba snake has a length of 3.30 m and a top speed of 4.90 m/s. Suppose a mongoose and a black mamba find themselves nose to nose. In an effort to escape, the snake accelerates past the mongoose at 7.82 m/s2 from rest. How much time ?top does it take the snake to reach its top speed? How far ?snake does the snake travel in that time? How much time ?react does the mongoose have to react before the black mamba's tail passes the mongoose's nose?