2NOTE: All of these equations require constant acceleration.

𝒗𝒐 = 𝒗𝒊 = 𝑰𝒏𝒊𝒕𝒊𝒂𝒍 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚

𝒗 = 𝒗𝒇 = 𝑭𝒊𝒏𝒂𝒍 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚

𝒂 = 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕

𝒅 = ∆𝒙 = 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕

𝒕 = 𝒕𝒊𝒎𝒆

Problem: How long does it take for a car to cross a 30.0m wide intersection after the light turns green. The car accelerates at a constant 2.00m/s2.

4

1. Write down the known values

2. 𝒗𝒊 = 𝟎

3. What equation should I use?

5

𝒗𝒐 = 𝟎. 𝟎𝒎/𝒔

𝒗 = ?

𝒂 = 𝟐. 𝟎𝟎𝒎/𝒔𝟐

𝒅 = 𝟑𝟎. 𝟎𝒎

𝒕 = ?

𝒅 =𝟏

𝟐𝒂𝒕𝟐, 𝟐 𝒅 = 𝒂𝒕𝟐,

𝟐(𝒅)

𝒂= 𝒕𝟐

𝒕 =𝟐(𝒅)

𝒂=

𝟐(𝟑𝟎.𝟎)

𝟐.𝟎𝟎= 𝟓. 𝟒𝟖𝒔

6

A plane must reach a speed of 33m/s for takeoff. How long of a runway is needed if the acceleration is 3.0m/s2?

HINT: I have velocity and acceleration, but I need displacement. Which equation should I use?

7

𝒗𝒐 = 𝟎𝒎/𝒔

𝒗 = 𝟑𝟑. 𝟎𝒎/𝒔

𝒂 = 𝟑. 𝟎𝟎𝒎/𝒔𝟐

𝒅 = ?

𝒕 = ?

𝒗𝟐 = 𝟐𝒂𝒅

𝒅 =𝒗𝒇𝟐

𝟐𝒂=

𝟑𝟑.𝟎𝟐

𝟐(𝟑.𝟎𝟎)= 𝟏𝟖𝟐𝒎

8

Problem: A car travelling at 100km/hexperiences a head-on collision and comes to a complete stop after compressing about 1.0m. How long does it take for the car to stop?

9

1. Write down known values

2. 𝒗𝒇 = 𝟎

3. Sometimes, 1 eqn is not enough…

10

𝒗𝒐 =𝟏𝟎𝟎𝒌𝒎

𝒉∗𝟏𝟎𝟎𝟎𝒎

𝟑𝟔𝟎𝟎𝒔= 𝟐𝟖𝒎/𝒔

𝒗 = 𝟎𝒎/𝒔

𝒂 = ?

𝒅 = 𝟏. 𝟎𝒎

𝒕 = ?

[EQ3] 𝒂 = −𝒗𝒊𝟐

𝟐∆𝒙= −

𝟐𝟖𝟐

𝟐.𝟎= −𝟑𝟗𝟎𝒎/𝒔𝟐

[EQ1] 𝒕 =𝒗𝒇−𝒗𝒊

𝒂=

𝟎−𝟐𝟖

−𝟑𝟗𝟎= 𝟎. 𝟎𝟕𝟐𝒔

11

EQN 0:

𝒅 = 𝒗𝒕

𝒗 =𝟎 + 𝟐𝟖𝒎/𝒔

𝟐= 𝟏𝟒𝒎/𝒔

𝒕 =𝒅

𝒗=

𝟏𝒎

𝟏𝟒𝒎/𝒔= 𝟎. 𝟎𝟕𝟏𝒔

A student throws a ball straight up in the air at 14.2 m/s. What is its velocity when it is 6.0 m above its point of release?

Hint: Acceleration due to gravity:

𝑔 = 9.8𝑚

𝑠2𝑑𝑜𝑤𝑛