Find the overall average speed of swimmer number one during the race.
Find the overall average speed of the second swimmer from the time he starts swimming until he ends his race.
What is the instantaneous speed of the second swimmer at time t = 25 s during the race?
What is the average acceleration of the second swimmer during the time interval starting at ti = 25 s and ending at tf = 50 s?
What is the average acceleration of the second swimmer during the time interval starting at ti = 25 s and ending at tf = 35 s?
What is the average acceleration of the first swimmer during the time interval starting at ti = 10 s and ending at tf = 30 s?
A car brakes from 60 mi/h to a full stop in 4 seconds. Find the acceleration of the car during this time interval in m/s2.
What distance did the car in problem 15 travel in the time since first applying the brakes?
A cheetah resting in the savanna sees her prey and accelerates from rest to 70 mi/h in 6.2 seconds. Assuming she moves with a constant acceleration, find this acceleration and the distance she ran when she first reaches 30 mi/h.
After what distance did the cheetah reach 70 mi/h?
Find the fall time for an object dropped from an altitude of 25,000 meters, neglecting air drag (i.e., the time it takes the bullet in the previous · example to return to the starting point, from the time it reached its maximum height).
Suppose the bullet is still effective in piercing sheet metal at a speed of 100 m/s. What is the maximum altitude at which you could still use this bullet to fight an aerial attack?
To find the depth of a well, you drop a small pebble and time its fall until you hear the splash of the pebble on the water surface below. What is the depth of the well if the time you got is 3.25 seconds? Consider that sound propagates almost instantaneously from the surface of the water to your ear.
What is the depth of the well if we take into account the finite sound speed in air of 334 m/s?
A mouse is dropped from an eagle's claws starting at an altitude of 150 meters. What distance does it fall in the first second after it is dropped?
What distance does the mouse in problem 23 travel in the third second of its free fall?
At what speed does the mouse in problem 23 hit the ground?
To answer these questions, we will need to use some basic physics formulas related to speed, acceleration, and distance. Here are the steps to find the solutions:
1. Find the overall average speed of swimmer number one during the race:
- Determine the total distance covered by swimmer number one during the race.
- Divide the total distance by the total time taken for the race.
2. Find the overall average speed of the second swimmer from the time he starts swimming until he ends his race:
- Determine the total distance covered by the second swimmer during this time interval.
- Divide the total distance by the time interval.
3. Find the instantaneous speed of the second swimmer at time t = 25 s during the race:
- Determine the distance covered by the second swimmer at time t = 25 s.
- Divide the distance by the time taken to cover that distance, which would be a very small time interval.
4. Find the average acceleration of the second swimmer during the time interval starting at ti = 25 s and ending at tf = 50 s:
- Determine the change in velocity of the second swimmer during this time interval.
- Divide the change in velocity by the time interval.
5. Find the average acceleration of the second swimmer during the time interval starting at ti = 25 s and ending at tf = 35 s:
- Follow the same steps as in step 4, but use the new time interval.
6. Find the average acceleration of the first swimmer during the time interval starting at ti = 10 s and ending at tf = 30 s:
- Follow the same steps as in step 4, but use the new time interval and the first swimmer's data.
7. Find the acceleration of the car during the time interval it takes to brake from 60 mi/h to a full stop in 4 seconds:
- Use the formula: acceleration = (change in velocity) / (time interval).
- Convert the velocity from miles per hour to meters per second, if required.
8. Find the distance travelled by the car in problem 7 since first applying the brakes:
- Use the formula: distance = (initial velocity) × (time) + (0.5) × (acceleration) × (time)^2.
9. Find the acceleration of the cheetah and the distance she ran when she first reaches 30 mi/h:
- Use the formula: acceleration = (final velocity - initial velocity) / (time).
- Use the formula: distance = (initial velocity) × (time) + (0.5) × (acceleration) × (time)^2.
10. Find the distance at which the cheetah reaches 70 mi/h:
- Use the formula: distance = (initial velocity) × (time) + (0.5) × (acceleration) × (time)^2.
11. Find the fall time for an object dropped from an altitude of 25,000 meters:
- Use the formula: time = square root((2 × distance) / (gravity)).
- Substitute the given value of distance and the appropriate value of gravity.
12. Find the maximum altitude at which the bullet is still effective in piercing sheet metal at a speed of 100 m/s:
- Use the formula: distance = (initial velocity)^2 / (2 × acceleration).
- Substitute the given value of initial velocity and the appropriate value of acceleration.
13. Find the depth of the well if the time for the pebble to fall is 3.25 seconds:
- Use the formula: distance = (1/2) × (acceleration × time^2) + sound_speed × time.
- Solve for distance, substituting the given time and sound speed.
14. Find the depth of the well, considering the finite sound speed in air:
- Use the formula from the previous step, but substitute the new sound speed value.
15. Find the distance the mouse falls in the first second after being dropped:
- Use the formula: distance = (1/2) × gravity × time^2.
- Substitute the given values of gravity and time.
16. Find the distance the mouse in problem 23 travels in the third second of its free fall:
- Use the formula from step 15, but substitute the new time value.
17. Find the speed at which the mouse in problem 23 hits the ground:
- Use the formula: speed = gravity × time.
- Substitute the given value of gravity and the appropriate value of time.