Two cars are traveling along a straight-line in the same direction, the lead car at 25.0 m/s and the other car at 32.0 m/s. At the moment the cars are 40.0 m apart, the lead driver applies the brakes, causing his car to have an acceleration of -2.20 m/s2.
(a) How much time does it take for the lead car to stop?
s
(b) Assuming that the chasing car brakes at the same time as the lead car, what must be the chasing car's minimum negative acceleration so as not to hit the lead car?
m/s2
(c) How much time does it take for the chasing car to stop?
s
See 9-22-11,5:59am post.
(a) To find the time it takes for the lead car to stop, we can use the kinematic equation:
v = u + at
where:
v = final velocity (0 m/s since the lead car stops)
u = initial velocity of the lead car (25.0 m/s)
a = acceleration of the lead car (-2.20 m/s^2)
t = time
Rearranging the equation to solve for time:
t = (v - u) / a
Substituting the values:
t = (0 - 25.0) / -2.20
t = 11.36 s
Therefore, it takes 11.36 seconds for the lead car to stop.
(b) To find the chasing car's minimum negative acceleration so as not to hit the lead car, we need to consider the relative velocity between the two cars. The chasing car is moving faster than the lead car, so it needs to have a negative acceleration to reduce its speed and avoid a collision.
The relative velocity between the two cars is the difference between their speeds:
relative velocity = chasing car's speed - lead car's speed
relative velocity = 32.0 m/s - 25.0 m/s
relative velocity = 7.0 m/s
The minimum negative acceleration of the chasing car required to prevent a collision is equal to the relative velocity divided by the time it takes for the lead car to stop:
acceleration = relative velocity / t
acceleration = 7.0 m/s / 11.36 s
acceleration = 0.616 m/s^2
Therefore, the chasing car's minimum negative acceleration to avoid hitting the lead car is 0.616 m/s^2.
(c) Since both cars will stop, the chasing car will have the same time to stop as the lead car. Therefore, it will also take 11.36 seconds for the chasing car to stop.