Besides the use of kinematic equations, these problems require careful reading, keen attention to units, analysis of multi-stage motions, multi-object comparisons, and complicated algebraic manipulations.
A biker speeds up to 28.0 m/s from rest in 6.42 seconds. The biker maintains this speed for 5.46 seconds before coasting to a stop in 8.8 seconds. What was the biker's average speed for the trip?
Average Speed
m/s
A red car moving at 59.7 mi/hr passes a blue car moving at 36.9 mi/hr. (Use 1609 m = 1 mile and 1 hr = 3600 s when converting to meters/second.) Seeing a stopped car in his lane up ahead, the driver of the red car applies the brakes just as he passes the blue car which causes the red car to slow down to a stop by losing 4.58 m/s every second. How much time (in seconds) passes before the two cars are side-by-side once again?
Time
s
A red car is sitting at a stop light at rest. When the light turns green, two things happen simultaneously:
(1) the red car accelerates to a speed of 29.4 m/s in 8.10 seconds and then maintains that 29.4 m/s speed, and
(2) a blue car passes by the red car at a constant speed of 20.8 m/s.
How much time will have elapsed from when the light turned green until the two cars are side-by-side?
It's breakfast time and Mr. H entertains himself once more by watching the daily beetle race across the 32.2-cm length of the Wheaties box top. Angie the beetle typically averages 3.49 mm/s and Bessie the beetle averages 5.23 mm/s. If Bessie gives Angie a 4.2 cm head start, ...
... then which beetle wins?
... when the winning beetle reaches the box's edge, how far (in cm) from the edge is the other beetle?
Winning Distance
cm
Ima Rushin can travel from Milwaukee Avenue to the school entrance gate at a constant speed of 20.4 m/s when the lights are green and there is no traffic. On Wednesday, Ima is stopped by a red light at Landwehr Road. She decelerates at -3.09 m/s/s, waits for 42.8 seconds before the light turns green and accelerates back up to speed at 4.19 m/s/s.
Determine the total time required to decelerate, stop, and accelerate back up to speed.
Total Time
Determine the amount of time the red light costs the driver (compared to if the car had not been stopped by the red light).
Time Lost
A tortoise and a hare are having a 1000-meter race. The tortoise runs the race at a constant speed of 2.55 cm/s. The hare moves at an average speed of 1.60 m/s for 10.0 minutes and then decides to take a nap. After waking up from the nap, the hare recognizes that the tortoise is about to cross the finish line and immediately accelerates from rest with a constant acceleration of 0.466 m/s/s for the remaining distance of the race. If the tortoise wins by a hair (no pun intended), then what is the time in hours that the hare napped?
Napping Time
hours
Hayden and Matthew are riding around the neighborhood on their scooters. Hayden is at rest when Matthew passes him moving at a constant speed of 0.462 m/s. After 1.53 seconds, Hayden decides to chase after Matthew, accelerating at 0.349 m/s/s. How much time elapses from when Hayden begins to accelerate and he is side-by-side with Matthew?