Calculating Distance Under Uniform Acceleration

Question:

A car accelerates uniformly from rest at 3 m/s² for 10 seconds. What distance does the car undergo during this acceleration?

a) 15 m
b) 30 m
c) 45 m
d) 60 m

Final answer:

The car travels 150 meters while uniformly accelerating from rest at 3 m/s² for 10 seconds, according to the equation s = 0.5at². The correct answer is not listed among the provided options.

Explanation:

To solve for the distance the car travels while it accelerates uniformly from rest, we can use the formula for distance under constant acceleration:

s = ut + ½at²

Where:

• s is the distance,
• u is the initial velocity,
• t is the time, and
• a is the acceleration.

Given that the initial velocity u is 0 (since the car starts from rest), the acceleration a is 3 m/s², and the time t is 10 seconds, the equation simplifies to:

s = ½(3 m/s²)(10 s)²

Therefore, the distance s that the car undergoes during this acceleration is:

s = ½(3 m/s²)(100 s²)

s = ½(300 m)

s = 150 m

So, the correct answer is none of the provided options (a) 15 m, (b) 30 m, (c) 45 m, or (d) 60 m. The distance traveled is actually 150 meters.