PLEASE ANSWER ASAP!!!!!!!!!! step by step
a) find the acceleration experienced by the driver of a car traveling at 50km/h if the car hits a pole and crumples 50cm.
b) repeat part a) for a car traveling 100km/h
See my previous answer to your same question.
cheers
Sure, I'll be glad to help you with that! Let's break it down step by step:
a) Finding the acceleration for a car traveling at 50 km/h and crumpling 50 cm:
Step 1: Convert the car's velocity from km/h to m/s.
To convert km/h to m/s, divide the speed by 3.6.
50 km/h ÷ 3.6 = 13.89 m/s
So, the velocity of the car is 13.89 m/s.
Step 2: Convert the crumpling distance from cm to m.
To convert cm to m, divide the distance by 100.
50 cm ÷ 100 = 0.5 m
So, the crumpling distance is 0.5 m.
Step 3: Use the formula for acceleration to find the value.
The formula for acceleration is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time taken.
In this case, the car comes to a stop when it hits the pole, so the final velocity (vf) is 0 m/s.
Since we don't have the time (t), we can use the formula vf^2 = vi^2 + 2ad, where a is the acceleration and d is the distance.
Substituting the known values:
0^2 = (13.89)^2 + 2a(0.5)
Step 4: Solve the equation for acceleration (a).
169.92 = 193.21 + a
Subtracting 193.21 from both sides:
169.92 - 193.21 = a
a ≈ -23.29 m/s^2
The negative sign indicates that the car experienced deceleration (decreasing velocity) while hitting the pole.
Therefore, the acceleration experienced by the driver of the car traveling at 50 km/h and crumpling 50 cm is approximately -23.29 m/s^2.
b) Finding the acceleration for a car traveling at 100 km/h and crumpling 50 cm:
Follow the same steps as above, considering a velocity of 100 km/h instead of 50 km/h.
Step 1: Convert the velocity from km/h to m/s.
100 km/h ÷ 3.6 = 27.78 m/s
Step 2: The crumpling distance is still 0.5 m.
Step 3: Use the formula vf^2 = vi^2 + 2ad.
Substituting the known values:
0^2 = (27.78)^2 + 2a(0.5)
Step 4: Solve the equation for acceleration (a).
a ≈ -65.64 m/s^2
Therefore, the acceleration experienced by the driver of the car traveling at 100 km/h and crumpling 50 cm is approximately -65.64 m/s^2.
I hope this helps! Let me know if you have any further questions.