In mud buggy driving, people attempt to drive an off road vehicle over a deep mud puddle. If the buggy stops before the end, it sinks into the mud and needs to be pulled out with a tow truck. A racer is driving his mud buggy in a straight line . when he hits the edge of the mud puddle, he is going 20m/s. When he gets to the other side of the 25m wide puddle he has slowed to 5m/s. Assuming constant acceleration what was the mud buggys acceleration while driving through the puddle and how long did it take to cross the puddle?

Question

In mud buggy driving, people attempt to drive an off road vehicle over a deep mud puddle. If the buggy stops before the end, it sinks into the mud and needs to be pulled out with a tow truck. A racer is driving his mud buggy in a straight line . when he hits the edge of the mud puddle, he is going 20m/s. When he gets to the other side of the 25m wide puddle he has slowed to 5m/s. Assuming constant acceleration what was the mud buggys acceleration while driving through the puddle and how long did it take to cross the puddle?

👇

2 answers
(click or scroll down)

👇

Answer 1

Steve answered
8 years ago

going across the puddle,

s = 20t - 1/2 at^2 = 25
v = 20 - at = 5

solve for a and t.

Answer 2

Explain Bot answered
11 months ago

To find the acceleration of the mud buggy while driving through the puddle, we can use the formula of acceleration:

acceleration (a) = (final velocity (v_f) - initial velocity (v_i)) / time (t)

In this case, the initial velocity (v_i) is 20 m/s, the final velocity (v_f) is 5 m/s, and we need to find the time taken to cross the puddle.

So, let's start by calculating the acceleration:

a = (v_f - v_i) / t

We know that v_i = 20 m/s, v_f = 5 m/s, and t is the time taken to cross the puddle. Now, we need to find the time.

With constant acceleration, we can use the formula of motion:

v_f^2 = v_i^2 + 2aΔx

Here, Δx represents the displacement or distance traveled, which is given as 25 m (width of the puddle).

Plugging in the values:

5^2 = 20^2 + 2a * 25

25 = 400 + 50a

25 - 400 = 50a

-375 = 50a

Now we can solve for the acceleration (a):

a = -375 / 50

a = -7.5 m/s^2

The mud buggy's acceleration while driving through the puddle is -7.5 m/s^2 (negative because it's slowing down).

To find the time taken to cross the puddle, we can use the equation of motion:

Δx = v_i * t + (1/2) * a * t^2

Since we know v_i = 20 m/s, a = -7.5 m/s^2, and Δx = 25 m, we can rearrange the equation:

25 = 20 * t + (1/2) * (-7.5) * t^2

25 = 20t - 3.75t^2

Rearranging again:

3.75t^2 - 20t + 25 = 0

Now, we can solve this quadratic equation to find the time (t).