How far does a motorcycle travel if it is moving at 15 m/s and then accelerates at a rate of 5 m/s² for 10 seconds?

Question image

Understand the Problem

The question is asking for the distance a motorcycle travels when it starts at a velocity of 15 m/s and accelerates at a rate of 5 m/s² for a duration of 10 seconds. To solve this, we will use the formula for distance under uniform acceleration: distance = initial velocity × time + 0.5 × acceleration × time².

Answer

The motorcycle travels $400 \, \text{m}$.
Answer for screen readers

The motorcycle travels a distance of $400 , \text{m}$.

Steps to Solve

  1. Identify the given values

We have the following values:

  • Initial velocity, $u = 15 , \text{m/s}$
  • Acceleration, $a = 5 , \text{m/s}^2$
  • Time, $t = 10 , \text{s}$
  1. Use the distance formula

The formula to calculate distance under uniform acceleration is: $$ d = ut + \frac{1}{2} at^2 $$

  1. Substitute the values into the formula

Plugging in the values we identified: $$ d = (15 , \text{m/s}) \cdot (10 , \text{s}) + \frac{1}{2} \cdot (5 , \text{m/s}^2) \cdot (10 , \text{s})^2 $$

  1. Calculate each term separately

Calculate the first term: $$ 15 , \text{m/s} \cdot 10 , \text{s} = 150 , \text{m} $$

Calculate the second term: $$ \frac{1}{2} \cdot 5 , \text{m/s}^2 \cdot 100 , \text{s}^2 = \frac{1}{2} \cdot 5 \cdot 100 = 250 , \text{m} $$

  1. Add the results to find the total distance

Now add both contributions to find the total distance: $$ d = 150 , \text{m} + 250 , \text{m} = 400 , \text{m} $$

The motorcycle travels a distance of $400 , \text{m}$.

More Information

The distance formula used here is derived from the kinematic equations, which describe motion under constant acceleration. Understanding this helps in solving problems related to various objects in motion.

Tips

  • Not squaring the time when calculating the second term.
  • Forgetting to convert units if necessary, such as ensuring the values are consistent (in this case, they are all in SI units).
  • Misreading the formula, which can lead to incorrect applications.
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