Chapter 2:

Linear Motion

Chapter 3:

Curvilinear Motion

Linear Motion

Horizontal Motion - motion along x-axis

Vertical Motion (Free-Falling Bodies) –motion along y-axis

Equation for Uniformly

Accelerated Linear Motion

S – Displacement

Vo – Initial Velocity a – acceleration

V – Final Velocity t – time elapsed

Example 1: Cars A and B approach each other on a straight

road from points 457 m apart. Car A has an initialspeed of 20 m/s and is decelerating at the rate of0.4 m/s2. Car B has an initial speed of 5 m/s and isaccelerating at the rate of 0.3 m/s2.

(a) When will the cars meet?

(b) How far will car A have travelled when theymeet?

(c) What will the speed of car A and car B bewhen they meet?

Example 2: Two cars start form rest at the same instant,

with care A initially at some distance behindcar B. Car A has a constant acceleration of 3.50m/s2 and car B an acceleration of 2.15 m/s2, CarA overtakes car B after car B has moved 40.2m(a) How much time does it take car A to

overtake car B?(b) How far was car A behind car B initially?(c) What is the speed of each car when car A

overtakes car B?

Example 3: A tortoise and a hare are in a road race to

defend the honor of their breed. The tortoisecrawls the entire 1000 meters at a speed of 0.2m/s. The rabbit runs the first 200 meters at 2m/s, stops to take a nap for 1.3 hours, andawakens to finish the last 800 meters with anaverage speed of 3 m/s. Who wins the raceand by how much time?

Example 4: Two cars start from rest from a gasoline

station at the same instant. They travel in thesame direction, both of them accelerating. Thefirst car has an acceleration whose magnitudeis 4.5 m/s2. The second car’s acceleration has amagnitude of 3.0 m/s2. Assuming straight-linemotion:(a) How much time passes until they are 2.5

km away from each other?(b) How far has the first car traveled then?(c) How far has the second car traveled then?

Example 5: A police car hidden at an intersection

observes a car that is moving with a constantspeed of 40 m/s. The police immediatelyaccelerated at 8 m/s2 and followed the car whenthe police was 50 m behind the car.

(a) When did the police catch up with the car?

(b) How far from the intersection did the policecatch up with the car?

(c) How fast was the police car traveling by thetime it caught up by the car?

Free-Falling Bodies

(Constant Acceleration)

S – Displacement

Vo – Initial Velocity g – gravity

V – Final Velocity t – time elapsed

Example 6: A missile is launched into the air at an initial

velocity of 80 m/s. it is moving with constantvelocity until it reached 1000 m, when the enginefails

(a) How long does it take it to reach 1000m?

(b) How high does the missile go?

(c) How long does it take for it to fall back to theearth?

(d) How long does it stay in the air?

(e) How fast is it going when it hits the ground?

Example 7: Suppose a small ball is thrown vertically

upward. It returns to its point of release with aspeed of 1960 cm/s. in the absence of airresistance:

(a) How long did it take the ball to reach itsmaximum height?

(b) To what maximum height did the ball rise?

(c) What was the ball’s velocity 1000 cm aboveits point of release?

Example 8: A ball is thrown vertically upwards, with an

initial speed of 50 ft/s, from the top of an 80-fttall school building. At the same instant, astudent is running on the ground at a distance of100 ft from the building.(a) What is the maximum height (with respect

to the ground) that the ball attains?(b) What is the speed of the ball when it reaches

the bottom of the building?(c) What must the average speed of the student

be if he is to catch the ball at the bottom of thebuilding?

Example 9: A rocket is fired vertically upwards with

initial velocity 80 m/s at the ground level. Itsengines then fire and it is accelerated at 4 m/s2

until it reaches an altitude of 1000 m. At thatpoint the engines fail and the rocket goes intofree-fall. Disregard resistance(a) How long was the rocket above the

ground?(b) What is the maximum altitude?(c) What is the velocity just before it collides

with the ground?

Example 10: A rock is dropped from rest into a well. The

sound of the splash is heard 4s after the rock isreleased from rest. How far below to top of thewell is the surface of the water? (Speed of soundin air at ambient temperature is 336 m/s).

Example 11: A rock is shot up vertically upward from the

edge of the top of the building. The rockreaches its maximum height 2 sec after beingshot. Then, after barely missing the edge of thebuilding as it falls downward, the rock strikesthe ground 8 sec after it was launched. Find;(a) Upward velocity the rock was shot at(b) The maximum height above the building

the rock reaches(c) Height of the building