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9.5 Equations of motion  (Page 2/3)

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A racing car is travelling north. It accelerates uniformly covering a distance of 725 m in 10 s. If it has an initial velocity of 10 m · s - 1 , find its acceleration.

  1. We are given:

    v i = 10 m · s - 1 Δ x = 725 m t = 10 s a = ?

  2. If you struggle to find the correct equation, find the quantity that is not given and then look for an equation that has this quantity in it.

    We can use equation [link]

    Δ x = v i t + 1 2 a t 2
  3. Δ x = v i t + 1 2 a t 2 725 m = ( 10 m · s - 1 × 10 s ) + 1 2 a × ( 10 s ) 2 725 m - 100 m = ( 50 s 2 ) a a = 12 , 5 m · s - 2

  4. The racing car is accelerating at 12,5 m · s - 2 north.

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A motorcycle, travelling east, starts from rest, moves in a straight line with a constant acceleration and covers a distance of 64 m in 4 s. Calculate

  1. its acceleration
  2. its final velocity
  3. at what time the motorcycle had covered half the total distance
  4. what distance the motorcycle had covered in half the total time.

  1. We are given:

    v i = 0 m · s - 1 ( because the object starts from rest. ) Δ x = 64 m t = 4 s a = ? v f = ? t = ? at half the distance Δ x = 32 m . Δ x = ? at half the time t = 2 s .

    All quantities are in SI units.

  2. We can use [link]

    Δ x = v i t + 1 2 a t 2
  3. Δ x = v i t + 1 2 a t 2 64 m = ( 0 m · s - 1 × 4 s ) + 1 2 a × ( 4 s ) 2 64 m = ( 8 s 2 ) a a = 8 m · s - 2 east

  4. We can use [link] - remember we now also know the acceleration of the object.

    v f = v i + a t
  5. v f = v i + a t v f = 0 m · s - 1 + ( 8 m · s - 2 ) ( 4 s ) = 32 m · s - 1 east

  6. We can use [link] :

    Δ x = v i + 1 2 a t 2 32 m = ( 0 m · s - 1 ) t + 1 2 ( 8 m · s - 2 ) ( t ) 2 32 m = 0 + ( 4 m · s - 2 ) t 2 8 s 2 = t 2 t = 2 , 83 s

  7. Half the time is 2 s, thus we have v i , a and t - all in the correct units. We can use [link] to get the distance:

    Δ x = v i t + 1 2 a t 2 = ( 0 ) ( 2 ) + 1 2 ( 8 ) ( 2 ) 2 = 16 m east
    1. The acceleration is 8 m · s - 2 east
    2. The velocity is 32 m · s - 1 east
    3. The time at half the distance is 2,83 s
    4. The distance at half the time is 16 m east
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Equations of motion

  1. A car starts off at 10 m · s - 1 and accelerates at 1 m · s - 2 for 10 s. What is its final velocity?
  2. A train starts from rest, and accelerates at 1 m · s - 2 for 10 s. How far does it move?
  3. A bus is going 30 m · s - 1 and stops in 5 s. What is its stopping distance for this speed?
  4. A racing car going at 20 m · s - 1 stops in a distance of 20 m. What is its acceleration?
  5. A ball has a uniform acceleration of 4 m · s - 1 . Assume the ball starts from rest. Determine the velocity and displacement at the end of 10 s.
  6. A motorcycle has a uniform acceleration of 4 m · s - 1 . Assume the motorcycle has an initial velocity of 20 m · s - 1 . Determine the velocity and displacement at the end of 12 s.
  7. An aeroplane accelerates uniformly such that it goes from rest to 144 km · hr - 1 in 8 s. Calculate the acceleration required and the total distance that it has traveled in this time.

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Source:  OpenStax, Siyavula textbooks: grade 10 physical science. OpenStax CNX. Aug 29, 2011 Download for free at http://cnx.org/content/col11245/1.3
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