Linear Kinematics -v = s/t - time rate change of position (m/s)

a = v/t - time rate change of velocity (m/s/s)

v - Change in velocity (in m/s)a - acceleration (in m/s/s)

Example: A car goes from 0 to 27 m/s in 9.0 seconds, what is its acceleration?(show math, units, meaning, m/s/s, m/s2, ms-2)

a = v/t, a = (27 m/s)/(9.0 s) = 3.0 m/s/s

3.0 m/s/s

Example: a = v/tA rocket accelerates at 4.5 “g” s. What time will it take to reach the speed of sound (Mach I = 343 m/s) from rest?

1 “g” = 9.81 m/s/sso 4.5 “g”s = (4.5)(9.81 m/s/s) = 44.145 m/s/sa = v/t, 44.145 m/s/s = (343 m/s)/tt = 7.7698…t = 7.8 s

t = 7.8 s

Whiteboards: Acceleration1 | 2 | 3 | 4 | 5

A car speeds up from 0 to 21 m/s in 5.3 seconds. What is their acceleration?

a = v/ta = (21 m/s)/(5.3 s) = 3.962264151 m/s/s4.0 m/s/s

4.0 m/s/s

A train can accelerate at .15 m/s/s. What time will it take to reach its top speed of 24 m/s from rest?

160 s

a = v/tv = 24 m/s, a = .15 m/s/s, .:. t = 160 s160 s

What is the final speed if a person accelerates from rest at 32 f/s/s for 2.7 seconds?

86 f/s

a = v/tt = 2.7 s, a = 32 f/s/s, .:. v = 86.4 f/s86 f/s

What is your acceleration if your velocity goes from 35 m/s to 20. m/s in 4.7 seconds?

-3.2 m/s/s

a = v/tv = -15 m/s, t = 4.7 s, .:. a = -3.1915-3.2 m/s/s

What is your final velocity if you are going 12 m/s and you accelerate at .48 m/s/s for the next 16 seconds?

20. m/s

a = v/ta = .48 m/s/s, t = 16 s, .:. v = 7.68 m/s12 m/s + 7.68 m/s = 19.68 m/s 20. m/s

Consider the this problem:

12 m/s + 7.68 m/s = 19.68 m/s u + at = v

New formula:

v = u + atu - initial velocityv - final velocitya - accelerationt - time elapsed

What is your final velocity if you are going 12 m/s and you accelerate at .48 m/s/s for the next 16 seconds?

Whiteboards: v = u + at

1 | 2 | 3 | 4 | 5

A car going 24.8 m/s decelerates at -2.451 m/s/s for 1.67 s. What is its final velocity?

v = u + atu = 24.8 m/s, a = -2.451 m/s/s, t = 1.67 s .:. v = 20.707 m/s20.7 m/s

20.7 m/s

What is the acceleration of a ball that goes from 12.5 m/s to 17.8 m/s in 2.5 seconds?

v = u + atu = 12.5 m/s, v = 17.8 m/s, t = 2.5 s .:. a = 2.12 m/s/s 2.1 m/s/s

2.1 m/s/s

A cop clocks a car going 22.4 m/s after having accelerated at -7.45 m/s/s for the last 3.4 seconds. What was the initial velocity of the car?

v = u + atv = 22.4 m/s, a = -7.45 m/s/s, t = 3.4 s .:. u = 47.73 m/s48 m/s

48 m/s

What time will it take a train to slow from 23.2 m/s to 14.8 m/s if the acceleration is -1.2 m/s/s?

v = u + atu = 23.2 m/s, v = 14.8 m/s, a = -1.2 m/s/s, .:. t = 7 s 7.0 s

7.0 s

A pitcher throws a ball at 34.2 m/s. The batter hits a line drive, hitting the ball 45.1 m/s back toward the pitcher. If the ball was in contact with the bat for .2153 seconds, what was its acceleration during that time? (Make the original direction the ball was traveling positive)

v = u + atu = +34.2 m/s, v = -45.1 m/s, t = .2153 s, .:. a = -368.32327 m/s/s -368 m/s/s

-368 m/s/s