Distance, Velocity & Acceleration - Practice
Sweet, Sweet Amigo
1) After driving for t hours the sweet, sweet Isuzu Amigo is
miles due east of its starting point (for 0 < t < 9).
a. Find its velocity at 2 hours.
b. Find its velocity at 8 hours.
c. Find its acceleration at 8 hours.
2) Vomit is upchucked vertically in the air to a height of
feet in t seconds.
a. Find the vomit's velocity in 9 seconds
b. Find the vomit's acceleration in 9 seconds.
a. Find the vomit's velocity in 9 seconds
b. Find the vomit's acceleration in 9 seconds.
3) A coconut is dropped from a European swallow while in flight. The height of the coconut after t seconds is
feet (neglecting air resistance and common sense, of course).
a. How long will it take the coconut to reach the ground?
b. What will the velocity of the coconut be when it impacts the ground?
African Swallows
Lice Population
Elijah's Profit
Pit's Armpits
Jeremy's Dash
1.b. At 8 hours, the sweet Amigo's velocity is 144 mph west.
1.c. At 8 hours, the sweet Amigo's velocity is decreasing by 66 mph every hour.
2.a. At 9 seconds, the vomit's velocity is 252 ft/sec upward.
2.b. At 9 seconds, the vomit's velocity is increasing by 55 ft/sec every second.
3.a. It will take approximately 3.46 seconds for the coconut to hit the ground.
3.b. When coconut's impact velocity is 110.72 ft/sec downward.
4.a. The coconut's impact velocity is 160 ft/sec downward.
4.b. The coconut's velocity is increasing by 32 ft/sec every second due to gravity.
5.a. On day 5 of being a dirtball, Mildred has approximately 76 lice on her head.
5.b. On the fifth day of being infested with scalp dwelling bugs, the number of lice on Mildred's head is increasing by about 30 lice per day.
5.c. On the fifth day of having lice, the growth rate of the lice on Mildred's head is increasing at a rate of about 6 lice per day, every day.
6.a. When Elijah has sold 3 sandals, his profit is about 5,729,387 denarii. (This is good for a company)
6.b. When Elijah has sold 3 sandals, his profit is decreasing by about 48,018 denarii per sandal sold. (This is bad for a company)
6.c. When Elijah has sold 3 sandals, his profit decline rate is slowing by about 423,429 denarii per sandal for every sandal sold. (This is good for a company)
7.a. Twelve minutes after playing UNO, the temperature of Pit's armpits are about 102 degrees F.
7.b. Twelve minutes after playing UNO, the temperature of Pit's armpits are increasing by .02 degrees F per minute.
7.c. Twelve minutes after playing UNO, the armpit's temperature's growth rate is slowing by about .003 degrees F per minute each minute.
8.a. Four seconds after the bells rings, Jeremy is 192 feet from room 226.
8.b. Four seconds after the bell rings, Jeremy's velocity is 64 feet per second.
8.c. Four seconds after the bell rings, Jeremy's velocity is slowing by 8 feet per second every second.
4) Two migratory African swallows are carrying a coconut on a line. After a synchronized dropping of the coconut on a Knight who says, "Ni", the coconut will fall a distance of
feet (neglecting air resistance, of course), where t is the time in seconds after the swallows' talons let go of the husk.
a. If it takes 5 seconds to hit the ground, find the impact velocity.
b. Find the acceleration due to gravity.
5) The population of lice chillin' on top of Mildred's head t days from now is predicted to be
a. Find P(5) and interpret your answer.
b. Find P'(5) and interpret your answer.
c. Find P"(5) and interpret your answer.
6) Elijah's profit from selling x sandals is predicted to be
million denarii.
a. Evaluate P(3) and interpret your answer.
b. Evaluate P'(3) and interpret your answer.
c. Evaluate P"(3) and interpret your answer.
7) The temperature of Pit's armpits t minutes after playing UNO is predicted to be H(t) = 102 - 3/t degrees Fahrenheit.
a. Find H(12) and interpret your answer.
b. Find H'(12) and interpret your answer.
c. Find H"(12) and interpret your answer.
8) The 5a bell rings, which is followed by Jeremy sprinting to lunch. His distance from room 226 t seconds after the bell ringing is
feet.
a. Find Jeremy's distance after 4 second using a sentence answer.
b. Find Jeremy's velocity after 4 second using a sentence answer.
c. Find Jeremy's acceleration after 4 second using a sentence answer.
ANSWERS.
1.a. At 2 hours, the sweet Amigo's velocity is 36 mph east.1.b. At 8 hours, the sweet Amigo's velocity is 144 mph west.
1.c. At 8 hours, the sweet Amigo's velocity is decreasing by 66 mph every hour.
2.a. At 9 seconds, the vomit's velocity is 252 ft/sec upward.
2.b. At 9 seconds, the vomit's velocity is increasing by 55 ft/sec every second.
3.a. It will take approximately 3.46 seconds for the coconut to hit the ground.
3.b. When coconut's impact velocity is 110.72 ft/sec downward.
4.a. The coconut's impact velocity is 160 ft/sec downward.
4.b. The coconut's velocity is increasing by 32 ft/sec every second due to gravity.
5.a. On day 5 of being a dirtball, Mildred has approximately 76 lice on her head.
5.b. On the fifth day of being infested with scalp dwelling bugs, the number of lice on Mildred's head is increasing by about 30 lice per day.
5.c. On the fifth day of having lice, the growth rate of the lice on Mildred's head is increasing at a rate of about 6 lice per day, every day.
6.a. When Elijah has sold 3 sandals, his profit is about 5,729,387 denarii. (This is good for a company)
6.b. When Elijah has sold 3 sandals, his profit is decreasing by about 48,018 denarii per sandal sold. (This is bad for a company)
6.c. When Elijah has sold 3 sandals, his profit decline rate is slowing by about 423,429 denarii per sandal for every sandal sold. (This is good for a company)
7.a. Twelve minutes after playing UNO, the temperature of Pit's armpits are about 102 degrees F.
7.b. Twelve minutes after playing UNO, the temperature of Pit's armpits are increasing by .02 degrees F per minute.
7.c. Twelve minutes after playing UNO, the armpit's temperature's growth rate is slowing by about .003 degrees F per minute each minute.
8.a. Four seconds after the bells rings, Jeremy is 192 feet from room 226.
8.b. Four seconds after the bell rings, Jeremy's velocity is 64 feet per second.
8.c. Four seconds after the bell rings, Jeremy's velocity is slowing by 8 feet per second every second.
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