Uniform Acceleration Problem: How Fast Can a Car Accelerate?

How fast can a car accelerate from rest to 20 m/s over a distance of 15 m?

Answer:

The car can accelerate from rest to 20 m/s over a distance of 15 meters in approximately 1.22 seconds.

Uniform acceleration problems involve calculating the rate at which an object speeds up over a certain distance. In this case, we are determining how quickly a car can accelerate from rest to a speed of 20 m/s while traveling a distance of 15 meters.

To find the time it takes for the car to cover this distance while accelerating uniformly, we can use the equation x = 0.5at², where 'x' is the distance, 'a' is acceleration, and 't' is time.

First, we need to solve for the acceleration 'a' using the formula a = (v - u) / t, where 'v' is the final velocity (20 m/s), 'u' is the initial velocity (0 m/s), and 't' is the time. Solving for 'a', we get a = (20 m/s - 0 m/s) / t = 20 m/s².

Substitute the values for distance (15 meters) and acceleration (20 m/s²) into the equation and solve for time 't': t = sqrt((2x)/a) = sqrt((2*15)/20) ≈ 1.22 seconds.

Therefore, the car can accelerate from rest to 20 m/s over a distance of 15 meters in approximately 1.22 seconds. This shows the capability of the car to achieve a considerable speed within a short distance.