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# Velocity and Acceleration

## The speed and direction of a moving object and how that rate changes over time.

Estimated9 minsto complete
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Progress
Practice Velocity and Acceleration
Progress
Estimated9 minsto complete
%
Velocity and Acceleration

Students will learn the meaning of acceleration, how it is different than velocity and how to calculate average acceleration.

### Key Equations

$v =$ velocity (m/s)

$v_i =$ initial velocity

$v_f =$ final velocity

$\Delta v =$ change in velocity $= v_f - v_i$

$v_{avg} = \frac{\Delta x}{\Delta t}$

$a =$ acceleration $(m/s^2)$

$a_{avg} = \frac{\Delta v}{\Delta t}$

Guidance
• Acceleration is the rate of change of velocity. So in other words, acceleration tells you how quickly the velocity is increasing or decreasing. An acceleration of $5 \ m/s^2$ indicates that the velocity is increasing by $5 m/s$ in the positive direction every second.
• Deceleration is the term used when an object’s speed (i.e. magnitude of its velocity) is decreasing due to acceleration in the opposite direction of its velocity.

#### Example 1

A Top Fuel dragster can accelerate from 0 to 100 mph (160 km/hr) in 0.8 seconds. What is the average acceleration in $m/s^2$ ?

Question: $a_{avg} = ? \ [m/s^2]$

Given: $v_i = 0 \ m/s$

${\;} \qquad \ \ v_f = 160 \ km/hr$

${\;} \qquad \ \quad t = 0.8 \ s$

Equation: $a_{avg} = \frac{\Delta v }{t}$

Plug n’ Chug: Step 1: Convert km/hr to m/s

$v_f = \left( 160 \frac{km}{hr} \right ) \left( \frac{1,000 \ m}{1 \ km} \right ) \left ( \frac{1 \ hr}{3,600 \ s} \right ) = 44.4 \ m/s$

Step 2: Solve for average acceleration:

$a_{avg} = \frac{\Delta v}{t} = \frac{v_f - v_i}{t} = \frac{44.4 \ m/s - 0 \ m/s}{0.8 \ s} = 56 \ m/s^2$

Answer: $\boxed {\mathbf{56 \ m/s^2}}$

### Time for Practice

1. Ms. Reitman’s scooter starts from rest and accelerates at $2.0 m/s^2$ . What is the scooter's velocity after 1s? after 2s? after 7s?

1. 2 m/s, 4 m/s, 14 m/s