Question 1

A motorist is traveling at $$18.0\ \mathrm{m/s}$$ when he sees a deer in the road $$38.0\ \mathrm{m}$$ ahead. If the maximum negative acceleration of the vehicle is $$-4.50\ \mathrm{m/s^2$}$$, what is the minimum reaction time $$\Delta t of $$the motorist that will allow him to avoid hitting the deer?

Accepted Answer

$$0.900\ \mathrm{s}$$

Question 2

A teenager has a car that speeds up at $$3.00\ \mathrm{m/s^2$}$$ and slows down at $$-4.50\ \mathrm{m/s^2$}. On a $$trip to the store, he accelerates from rest to $$12.0\ \mathrm{m/s}$$, drives a constant speed for $$50.0\ \mathrm{m}$$, then comes to a momentary stop at a crosswalk. How far does the teenager travel during the acceleration phase?

Accepted Answer

$$24.0\ \mathrm{m}$$

Question 3

A ball is dropped from rest from a height $$h$$ above the ground. Another ball is thrown vertically upward from the ground at the same instant the first ball is released. Determine the speed of the second ball if the two balls are to meet at height $$h/2$$ above the ground.

Accepted Answer

$$\sqrt{gh/2}$$

Question 4

A fan observes that it takes $$1.50\ \mathrm{s}$$ for a ball to reach its maximum height after being struck by a bat. What is the initial velocity of the ball?

Accepted Answer

$$14.7\ \mathrm{m/s}$$

Question 5

A woman is reported to have fallen $$144\ \mathrm{ft}$$ from the 17th floor of a building, landing on a metal ventilator box, which she crushed to a depth of $$1.80\ \mathrm{ft}. $$Calculate her speed just before she collided with the ventilator box. (Use $$g = 32.2\ \mathrm{ft/s^2$}.)$$

Accepted Answer

$$96.0\ \mathrm{ft/s}$$

Question 6

After falling $$144\ \mathrm{ft}$$, the woman crushes the ventilator box to a depth of $$1.80\ \mathrm{ft}. $$What is her average acceleration while in contact with the box?

Accepted Answer

$$-2560\ \mathrm{ft/s^2$}$$

Question 7

A car and train move together along parallel paths at $$25.0\ \mathrm{m/s}$$, with the car adjacent to the rear of the train. The car undergoes a uniform acceleration of $$-2.00\ \mathrm{m/s^2$}$$ and comes to rest. It remains at rest for $$5.0\ \mathrm{s}$$ and then accelerates back to a speed of $$25.0\ \mathrm{m/s} at a $$rate of $$2.00\ \mathrm{m/s^2$}. $$How far behind the rear of the train is the car when it reaches the speed of $$25.0\ \mathrm{m/s}$$ again, assuming the train has maintained $$25.0\ \mathrm{m/s}$$?

Accepted Answer

$$150\ \mathrm{m}$$

Question 8

A motorist traveling at $$18.0\ \mathrm{m/s}$$ sees a deer $$38.0\ \mathrm{m}$$ ahead. If his reaction time is $$0.900\ \mathrm{s}$$, how far will he travel before he hits the deer, assuming maximum braking acceleration of $$-4.50\ \mathrm{m/s^2$}$$?

Accepted Answer

$$44.5\ \mathrm{m}$$

Question 9

A ball is thrown vertically upward with an initial velocity $$v_0. $$What is the time required for the ball to reach its maximum height?

Accepted Answer

$$t = \dfrac{v_0$}{g}$$

Question 10

A car accelerates from rest at $$3.00\ \mathrm{m/s^2$} to$$ $$12.0\ \mathrm{m/s}$$, then travels at constant speed for $$50.0\ \mathrm{m}$$, and finally decelerates at $$-4.50\ \mathrm{m/s^2$} to $$rest. What is the total distance traveled by the car?

Accepted Answer

$$74.0\ \mathrm{m}$$

Question 11

A woman falls $$144\ \mathrm{ft}$$ and crushes a ventilator box to a depth of $$1.80\ \mathrm{ft}. $$How much time did it take her to crush the box?

Accepted Answer

$$0.075\ \mathrm{s}$$

Question 12

A ball is dropped from a height $$h. $$What is the velocity of the ball just before it hits the ground?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 13

A car accelerates from rest at $$2.00\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}$$, then travels at constant speed for $$10.0\ \mathrm{s}$$, and finally decelerates at $$-2.00\ \mathrm{m/s^2$} to $$rest. What is the total distance traveled?

Accepted Answer

$$125\ \mathrm{m}$$

Question 14

A ball is thrown upward with an initial velocity of $$14.7\ \mathrm{m/s}. $$What is the maximum height it reaches?

Accepted Answer

$$11.0\ \mathrm{m}$$

Question 15

A car moving at $$25.0\ \mathrm{m/s}$$ decelerates at $$-2.00\ \mathrm{m/s^2$}$$ until it comes to rest. How far does it travel during this time?

Accepted Answer

$$156\ \mathrm{m}$$

One-Dimensional Kinematics: Study Notes and Problem Analysis

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