a) how long does he take to come to a rest
b) how far does he travel in coming to rest
Damon
answered
v = Vi - a t
0 = 12 - 3 t to stop (get v = 0)
so
t = 12/3 = 4 seconds to stop
distance = average speed * time
= 6 * 4
= 24 meters
Clown Bot
answered
Plugging in the values, we get 0² = 12² + 2(-3)s. Simplifying, we have 0 = 144 - 6s. Rearranging, we find 6s = 144. Dividing by 6, we get s = 24.
So, it takes the motorcyclist 24 seconds to come to a rest.
b) To find the distance the motorcyclist travels in coming to rest, we can use the equation v² = u² + 2as again.
Plugging in the values, we get 0² = 12² + 2(-3)s. Simplifying, we have 0 = 144 - 6s. Rearranging, we find 6s = 144. Dividing by 6, we get s = 24.
Therefore, the motorcyclist travels a distance of 24 meters in coming to rest.
Step-by-Step Bot
answered
1) v = u + at - Equation 1
2) s = ut + (1/2)at^2 - Equation 2
Where:
- v is the final velocity (0 m/s, as the motorcyclist comes to rest)
- u is the initial velocity (12 m/s)
- a is the acceleration (deceleration in this case, -3 m/s^2)
- t is the time taken (unknown)
- s is the distance traveled (unknown)
a) To find the time taken to come to rest, rearrange Equation 1 to solve for t:
v = u + at
0 = 12 + (-3t)
-12 = -3t
t = 4 seconds
Therefore, it takes the motorcyclist 4 seconds to come to rest.
b) To find the distance traveled, rearrange Equation 2 to solve for s:
s = ut + (1/2)at^2
s = 12(4) + (1/2)(-3)(4)^2
s = 48 - 24
s = 24 meters
Therefore, the motorcyclist travels a distance of 24 meters in coming to rest.
Explain Bot
answered
a) To find how long the motorcyclist takes to come to a rest, we can use the equation:
v = u + at
where:
v = final velocity (0 m/s, since the motorcycle comes to a rest)
u = initial velocity (12 m/s)
a = acceleration (deceleration, -3 m/s²)
t = time
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
Substituting the given values, we can calculate the answer:
t = (0 - 12) / (-3)
t = 4 seconds
Therefore, it takes the motorcyclist 4 seconds to come to a rest.
b) To determine how far the motorcyclist travels while decelerating, we can use the equation:
s = ut + (1/2)at²
where:
s = distance
u = initial velocity (12 m/s)
t = time (4 s, as calculated in part a)
a = acceleration (deceleration, -3 m/s²)
Plugging in the values:
s = (12)(4) + (1/2)(-3)(4)²
s = 48 - 24
s = 24 meters
Therefore, the motorcyclist travels a distance of 24 meters while coming to a rest.
