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Velocity and Acceleration

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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.
  • Gravity near the Earth pulls an object downwards toward the surface of the Earth with an acceleration of 9.8 \ m/s^2 ( \approx 10 \ m/s^2) . In the absence of air resistance, all objects will fall with the same acceleration. The letter g is used as the symbol for the acceleration of gravity.
    • When talking about an object's acceleration, whether it is due to gravity or not, the acceleration of gravity is sometimes used as a unit of measurement where 1g=9.8m/s^2 . So an object accelerating at 2g's is accelerating at 2*9.8m/s^2 or 19.6m/s^2
  • 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}} Note that this is over 5 \frac{1}{2} g’s!

Watch this Explanation

You can download this simultion and play around on it a bit to see the principles in action.  

The Moving Man (PhET Simulation)

Time for Practice

  1. Ms. Reitman’s scooter starts from rest and accelerates at 2.0 m/s^2 .
    1. Where will the scooter be relative to its starting point after 7.0 seconds?
    2. What is the scooter's velocity after 1s? after 2s? after 7s?
  2. Below are images from a race between Ashaan (above) and Zyan (below), two daring racecar drivers. High speed cameras took four pictures in rapid succession. The first picture shows the positions of the cars at t = 0.0 . Each car image to the right represents times 0.1, 0.2, and 0.3 seconds later.
    1. Who is ahead at t = 0.2 \;\mathrm{s} ? Explain.
    2. Who is accelerating? Explain.
    3. Who is going fastest at  t = 0.3 \;\mathrm{s} ? Explain.
    4. Which car has a constant velocity throughout? Explain.
    5. Graph x vs. t and v vs. t . Put both cars on same graph; label which line is which car.
    6. Which car is going faster at t = 0.2 \;\mathrm{s} (Hint: Assume they travel the same distance between 0.1 and 0.2 seconds)?

Answers

1. a. 49 m b. 2 m/s, 4 m/s, 14 m/s

2. See Video above

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