Calculating Distance Traveled by a Car Under Constant Acceleration
When a car accelerates from an initial velocity (u) to a final velocity (v) in a given time (t), we can use the principles of physics to calculate the distance (s) it travels. This article will walk you through the steps to find the distance traveled by a car that accelerates from 5 m/s to 20 m/s in 10 seconds.
Understanding the Physics Behind the Calculation
The first step is to recall the basic formula for distance under constant acceleration:
distance (s) initial velocity (u) × time (t) 1/2 × acceleration (a) × time2
Given that the car starts from rest, the initial velocity (u) is 0 m/s, and the final velocity (v) is 20 m/s, with a time (t) of 10 seconds. We can calculate the acceleration (a) first.
Calculating Acceleration
The formula for acceleration is:
acceleration (a) (final velocity (v) - initial velocity (u)) / time (t)
Substituting the given values:
a (20 m/s - 0 m/s) / 10 s 2 m/s2
Using the Distance Formula
Now, let's substitute the values into the distance formula:
distance (s) ut 1/2 × a × t2
Substituting u 0, a 2 m/s2, and t 10 s:
s 0 m/s × 10 s 1/2 × 2 m/s2 × (10 s)2
Calculating each part:
0 m/s × 10 s 0 m 1/2 × 2 m/s2 × 100 s2 100 mAdd these two results together:
s 0 m 100 m 100 m
Thus, the distance traveled by the car is 100 meters.
Verifying the Solution with Different Methods
Another method to find the distance is to use the formula for acceleration and the distance traveled:
acceleration (a) (final velocity (v) - initial velocity (u)) / time (t)
Substituting the given values:
a (20 m/s - 0 m/s) / 10 s 2 m/s2
Now, to find the distance:
distance (s) 1/2 × a × t2
Substituting a 2 m/s2 and t 10 s:
s 1/2 × 2 m/s2 × (10 s)2
Calculating:
s 1/2 × 2 m/s2 × 100 s2 100 m
This confirms that the car travels 100 meters.
Conclusion
By using the basic principles of physics and the appropriate formulas, we have calculated the distance traveled by a car that accelerates from 5 m/s to 20 m/s in 10 seconds. This method can be applied to similar physics problems involving constant acceleration.