Question

If a car accelerates from rest at a constant 3.0 m/s²:

A. How long (time) will be required to reach 15 m/s?
B. What distance does the car travel in the 15 minutes?

Answer 1

It will take the car 5 seconds to reach a speed of 15 m/s from rest at a constant acceleration of 3.0 m/s². In that time, the car will travel a distance of 37.5 meters.

Step-by-step explanation:

If a car accelerates from rest at a constant 3.0 m/s², to calculate the time required to reach 15 m/s, you can use the formula for constant acceleration:

final velocity (v) = initial velocity (u) + acceleration (a) × time (t)

Since the car starts from rest, the initial velocity (u) is 0, so the formula simplifies to:

v = a × t

Now, we can solve for time (t):

15 m/s = 3.0 m/s² × t

t = 15 m/s / 3.0 m/s²

t = 5 seconds

To determine the distance traveled in that time, we can use the formula:

distance (d) = u × t + ½ a × t²

Since u is 0, the formula simplifies to:

d = ½ × 3.0 m/s² × (5 s)²

d = ½ × 3.0 m/s² × 25 s²

d = 37.5 meters

Therefore, it will take the car 5 seconds to reach 15 m/s, and it will have traveled a distance of 37.5 meters in that time.