Question

If a pronghorn antelope accelerates from rest in a straight line with a constant acceleration of \(1.7 \mathrm{m} / \mathrm{s}^{2}\) how long does it take for the antelope to reach a speed of \(22 \mathrm{m} / \mathrm{s} ?\)

Short answer

Answer: It takes approximately 12.94 seconds for the antelope to reach a speed of 22 m/s.

Step-by-step solution

Write down the given information

We are given the following information: - Initial speed (v_i): 0 m/s - Final speed (v_f): 22 m/s - Acceleration (a): 1.7 m/s²

Write down the equation

We will use the equation of motion that relates the initial speed, final speed, acceleration, and time: \(v_f = v_i + at\)

Plug in the given values

We can now plug in the given values into our equation. Since the antelope starts from rest, its initial speed is 0 m/s: \(22 \mathrm{m} / \mathrm{s} = 0 + (1.7 \mathrm{m} / \mathrm{s}^{2})(t)\)

Solve for time (t)

To solve for time, we need to isolate t on one side of the equation. Divide both sides of the equation by the acceleration value (1.7 m/s²): \(\frac{22 \mathrm{m} / \mathrm{s}}{1.7 \mathrm{m} / \mathrm{s}^{2}} = t\) Calculate the value of t: \( t\approx 12.94 \, s\)

Write down the final answer

It will take approximately \(12.94\) seconds for the antelope to reach a speed of \(22 \mathrm{m} / \mathrm{s}\).