The Physics
Hypertextbook
Opus in profectus

# Acceleration

## Problems

### practice

1. A problem about a car (US version).
1. A car is said to go "zero to sixty in six point six seconds". What is its acceleration in m/s2?
2. The driver can't release his foot from the gas pedal (a.k.a. the accelerator). How many additional seconds would it take for the driver to reach 80 mph assuming the aceleration remains constant?
3. A car moving at 80 mph has a speed of 35.8 m/s. What acceleration would it have if it took 5.0 s to come to a complete stop?
2. A baseball is pitched at 40 m/s (90 mph) in a Major League game. The batter hits the ball on a line drive straight toward the pitcher at 50 m/s (112 mph). Determine the the acceleration of the ball if it was in contact with the bat for 130 s.

### conceptual

1. Which device(s) on a car can be used to control its acceleration?
2. Describe a situation when an object has…
1. zero velocity, but non-zero acceleration
2. zero acceleration, but non-zero velocity

### numerical

1. At main engine cutoff (MECO), the Space Shuttle is at an altitude of 113 km (70 miles), traveling 7,600 m/s (17,000 mph) relative to the Earth. This occurs 7 minutes 40 seconds into the mission. Determine the magnitude of the average acceleration experienced by the shuttle astronauts from lift off to MECO.
2. Most roller coasters are towed to the top of a large hill by means of a motor driven chain and released at the start of their run. This "chain link lift hill" technology is simple to design and quite reliable, but will never be able to accelerate the coaster faster than 1 g. In the quest to build new and ever more terrifying thrill rides, some designers have employed alternate acceleration methods. Two such roller coasters are described below.
1. The Flight of Fear is accelerated using linear induction motors (LIM), which generate a sequentially moving magnetic wave that propels the coaster like a surfer. A pair of LIMs is 85.3 m (280 foot) long and can accelerate the coaster to 24 m/s (54 mph) in 3.9 s. Determine the magnitude of the starting acceleration (in g) of the Flight of Fear.
2. The HyperSonic XLC (Extreme Launch Coaster) was the world's first roller coaster to be launched using compressed air. Four, 150 kW (200 hp) compressed air motors accelerated the eight seat coaster from zero to 36 m/s (80 mph) in 1.8 s. Determine the magnitude of the starting acceleration (in g) of the Hypersonic XLC.
3. When ejection seats were being developed, it was not known if a human could survive the intense acceleration needed to clear a jet fighter in an emergency. In 1954, US Air Force Colonel John Stapp was strapped into the seat of a rocket sled and blasted across the New Mexico desert at 282 m/s (632 mph) to examine the physiological effects of high speed ejection. The sled traveling at eight-tenths the speed of sound, a land speed record at that time, was then guided into a large trough of water, stopping it in a mere 1.4 s. Determine the magnitude of the average acceleration during the critical portion of this experiment. (Colonel Stapp subjected himself to several extreme acceleration experiments and survived all of them relatively unharmed.)
4. US Federal Motor Vehicle Safety Standard No. 208 specifies performance requirements for the protection of vehicle occupants in crashes. In an auto accident, passengers and drivers should not experience an average head acceleration of more than 60 g for longer than 36 milliseconds. At what speed did the authors of this standard assume a typical, serious, survivable auto accident would take place?
5. During a typical accident, a properly designed bicycle helmet should keep acceleration of the head below 200 g for a cumulative duration of three milliseconds and 150 g for a cumulative duration of six milliseconds. At what speed did the authors of this standard assume a typical accident would take place?
6. A distressed car is rolling backward, downhill at 3.0 m/s when its driver finally manages to get the engine started. What velocity will the car have 6.0 s later if it can accelerate at 3.0 m/s2?
7. What zero-to-sixty time is equivalent to an average acceleration of 1 g?