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?
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
- Identify the given values
We have the following values:
- Initial velocity, $u = 15 , \text{m/s}$
- Acceleration, $a = 5 , \text{m/s}^2$
- Time, $t = 10 , \text{s}$
- Use the distance formula
The formula to calculate distance under uniform acceleration is: $$ d = ut + \frac{1}{2} at^2 $$
- Substitute the values into the formula
Plugging in the values we identified: $$ d = (15 , \text{m/s}) \cdot (10 , \text{s}) + \frac{1}{2} \cdot (5 , \text{m/s}^2) \cdot (10 , \text{s})^2 $$
- Calculate each term separately
Calculate the first term: $$ 15 , \text{m/s} \cdot 10 , \text{s} = 150 , \text{m} $$
Calculate the second term: $$ \frac{1}{2} \cdot 5 , \text{m/s}^2 \cdot 100 , \text{s}^2 = \frac{1}{2} \cdot 5 \cdot 100 = 250 , \text{m} $$
- 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.