Question

The formula for final velocity of an object starting from zero and undergoing constant acceleration is v=1/2at^2, what is the time it will take a car accelerating at 4 m/s^2 to reach 50m/s

Answer 1

Answer on Question #68167 – Math – Algebra

Question

The formula for final velocity of an object starting from zero and undergoing constant acceleration is $v = 1/2at^2$, what is the time it will take a car accelerating at $4 \, \text{m/s}^2$ to reach $50 \, \text{m/s}$

Solution

The formula for final velocity of an object starting from zero and undergoing constant acceleration is

$$v = \frac{1}{2} \cdot a \cdot t^2,$$

where $a$ is acceleration, $t$ is time, $v$ is velocity.

It follows from this equation that

$$t^2 = \frac{2v}{a},$$ $$t = \sqrt{\frac{2v}{a}}.$$

Substitute $v = 50 \, (\text{m/s})$, $a = 4 \, (\text{m/s}^2)$ into the previous formula:

$$t = \sqrt{\frac{2 \cdot 50}{4}} = \sqrt{25} = 5 \, (\text{s})$$

Answer: It will take 5 seconds.

Answer provided by https://www.AssignmentExpert.com