Question

A car moving at a straight line has an initial velocity of 6 m/s when it begins to be accelerated at 1.5 m/s^2. How long would it take to reach a velocity of 20 m/s and how far would the car travel?

Answer 1

To solve this problem, we can use the following kinematic equations:

1. Final velocity (v) = Initial velocity (u) + (Acceleration (a) * Time (t))
2. Distance (s) = Initial velocity (u) * Time (t) + (0.5 * Acceleration (a) * Time (t)^2)

Given: Initial velocity (u) = 6 m/s Acceleration (a) = 1.5 m/s^2 Final velocity (v) = 20 m/s

Let's calculate the time it takes to reach a velocity of 20 m/s:

Using equation 1: 20 m/s = 6 m/s + (1.5 m/s^2 * t)

Simplifying the equation: 20 m/s - 6 m/s = 1.5 m/s^2 * t 14 m/s = 1.5 m/s^2 * t

Dividing both sides by 1.5 m/s^2: t = 14 m/s / 1.5 m/s^2 t ≈ 9.33 seconds

Therefore, it would take approximately 9.33 seconds for the car to reach a velocity of 20 m/s.

Now, let's calculate the distance traveled during this time:

Using equation 2: s = 6 m/s * t + (0.5 * 1.5 m/s^2 * t^2) s = 6 m/s * 9.33 s + (0.5 * 1.5 m/s^2 * (9.33 s)^2)

Simplifying the equation: s = 55.98 m + 62.18 m s ≈ 118.16 meters

Therefore, the car would travel approximately 118.16 meters during this time.