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?

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2 answers
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Answer 1

Henry answered
8 years ago

V^2 = Vo^2 + 2a*d.

5^2 = 20^2 + 2a*25.
2a*25 = -375, a = -7.5 m/s^2.

V = Vo + a*t.
5 = 20 - 7.5t, t = 2 s.

Answer 2

Explain Bot answered
11 months ago

To find out the mud buggy's acceleration while driving through the puddle and the time it took to cross it, we can use the equations of motion.

Given:
Initial velocity (u) = 20 m/s
Final velocity (v) = 5 m/s
Distance (s) = 25 m

We need to find:
Acceleration (a) and Time (t)

We can use the equation which relates the final velocity, initial velocity, acceleration, and time:

v = u + at

Rearranging the equation, we get:

a = (v - u) / t

To find the time (t) taken to cross the puddle, we can use the equation which relates velocity, distance, and time:

s = ut + (1/2)at^2

Plugging in the values, we get:

25 = 20t + (1/2)at^2

Now we have two equations with two unknowns (a and t). We can solve the equations simultaneously to find the values.

First, let's find the value of acceleration (a):

a = (v - u) / t
a = (5 - 20) / t
a = -15 / t

Now substitute this value in the second equation:

25 = 20t + (1/2)(-15/t)t^2
25 = 20t - (15/2)t
25 = (40t - 15t) / 2

Simplifying, we get:

25 = 25t / 2
t = 2 seconds

Now we can substitute the value of time in either of the equations to find acceleration:

a = (v - u) / t
a = (5 - 20) / 2
a = -15 / 2
a = -7.5 m/s^2

Therefore, the mud buggy's acceleration while driving through the puddle was -7.5 m/s^2 (negative because it is slowing down), and it took 2 seconds to cross the puddle.