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 20 m/s. when he gets to the other side of the 25 m wide puddle he has slowed to 5m/s.
Assuming a constant acceleration, what was the mud buggy's acceleration while driving through the puddle and how long would it take to cross the puddle?
See previous post: Sun, 9-18-16, 6:50 PM.
To find the mud buggy's acceleration while driving through the puddle, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity (5 m/s)
- u is the initial velocity (20 m/s)
- a is the acceleration
- s is the displacement (25 m)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
a = (5^2 - 20^2) / (2 * 25)
a = (25 - 400) / 50
a = -375 / 50
a = -7.5 m/s^2
The negative sign indicates that the mud buggy is decelerating.
To calculate the time it takes to cross the puddle, we can use the formula:
v = u + at
Where:
- v is the final velocity (5 m/s)
- u is the initial velocity (20 m/s)
- a is the acceleration (-7.5 m/s^2)
- t is the time
Rearranging the equation, we have:
t = (v - u) / a
t = (5 - 20) / (-7.5)
t = -15 / (-7.5)
t = 2 seconds
So, the mud buggy's acceleration while driving through the puddle is -7.5 m/s^2, and it takes 2 seconds to cross the puddle.