Question

A car is driving at 100.0 mph and a buffalo steps out into the road 101 meters ahead. The car can accelerate at -5.00 m/s2 . Will the car be able to stop in time before hitting the buffalo?

a) Yes
b) No
c) Depends on the car's size
d) Depends on the buffalo's speed

Answer 1

The car traveling at 100.0 mph (44.7 m/s) with an acceleration of -5.00 m/s^2 cannot stop in 101 meters; the stopping distance is calculated to be 200.49 meters which exceeds the distance to the buffalo.

Step-by-step explanation:

The student's question is about determining whether a car traveling at 100.0 mph can stop in time before hitting a buffalo at a distance of 101 meters, assuming the car has a deceleration of -5.00 m/s2. First, let's convert the car's speed to meters per second:

100.0 mph = 44.7 m/s (1 mph ≈ 0.44704 m/s)

Next, we can use the equation of motion v2 = u2 + 2as to determine if the car can stop, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance. The final velocity v will be 0 since the car aims to stop, so we're left with:

0 = (44.7 m/s)2 + 2(-5.00 m/s2)(s)

Solving for s, the stopping distance:s = (44.7 m/s)2 / (2 * 5.00 m/s2) = 200.49 m

The stopping distance is 200.49 m, which is greater than the distance to the buffalo (101 m). Therefore, the car will not be able to stop in time, so the answer to the student's question is (b) No.