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8.3 The acceleration of a racing car is 12 m/s². The racing car reaches 150 km/h from rest.

Calculate:

8.3.1 The time it takes to reach its final velocity.
8.3.2 The distance it covered to reach 150 km/h.

Answer :

To solve these problems, we will use the equations of motion for constant acceleration.

Given data:

  • Initial velocity [tex]u = 0[/tex] m/s (since the car starts from rest)
  • Final velocity [tex]v = 150[/tex] km/h
  • Acceleration [tex]a = 12[/tex] m/s²

First, let's convert the final velocity from km/h to m/s since standard units for these calculations are in meters per second.

[tex]1 \text{ km/h} = \frac{1}{3.6} \text{ m/s}[/tex]

Therefore, [tex]150 \text{ km/h}[/tex] is:

[tex]v = 150 \times \frac{1}{3.6} = 41.67 \text{ m/s (approximately)}[/tex]

8.3.1 The time it takes to reach its final velocity:

We use the equation of motion:

[tex]v = u + at[/tex]

Substitute the given data:

[tex]41.67 = 0 + 12t[/tex]

Solve for [tex]t[/tex]:

[tex]41.67 = 12t \\
t = \frac{41.67}{12} = 3.4725 \\approx 3.47 \text{ seconds}[/tex]

8.3.2 The distance it covered to reach 150 km/h:

We use another equation of motion:

[tex]s = ut + \frac{1}{2}at^2[/tex]

Substitute the known values:

[tex]s = 0 \times 3.47 + \frac{1}{2} \times 12 \times (3.47)^2[/tex]

Calculate [tex]s[/tex]:

[tex]s = 0 + 6 \times 12.0481 \\
s = 72.29 \text{ meters (approximately)}[/tex]

Therefore, it takes approximately 3.47 seconds for the racing car to reach its final velocity, and the distance covered is approximately 72.29 meters.

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