a box of lollipops accidentally falls from the back of a truck and hits the ground with a speed of 15 m/s. it slides along the ground for a distance of 45 m before coming to rest. determine
a) the length of time the box slides from stopping
b)the time it takes to slide 10.0 meters
a. Average velocity: 15/2=7.5m/s, time= distanc/avgvelociyt= 45/7.5 sec
b. 10 m? at the start, or near the end? Assuming the first 10 m
distance= vi*time-1/2 a t^2
so first determine acceleration: a= changevlocyt/time=-15/(45/7.5)= -2.5m/s^2
10=15*time-2.5/2 time ^2 so a quadratic. In standard form...
1.25t^2-15t +10=0
t= (15+-sqrt(225-50)/2.5=6 +-sqrt175 /2.5= 11.6, 0.709, and reject the 11.6 because it is greater than the time to stop. tme= .709 seconds
oops, i meant the last 10 meters. do i just have to subtract instead of adding the 1/2 a t^2
To find the answers to these questions, we can use the equations of motion. Specifically, we will use the equation:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s, as the box comes to rest)
u = initial velocity (15 m/s)
a = acceleration (unknown)
s = displacement (45 m)
a) To find the length of time the box slides from stopping, we need to determine the acceleration (a) first.
Rearranging the equation:
a = (v^2 - u^2) / 2s
Plug in the known values:
a = (0^2 - 15^2) / (2 * 45)
Simplifying:
a = (-225) / 90
a = -2.5 m/s^2
The negative sign indicates that the acceleration is in the opposite direction of motion (deceleration). Now, we can find the time (t) using another equation:
v = u + at
Rearranging:
t = (v - u) / a
Plug in the known values:
t = (0 - 15) / (-2.5)
Simplifying:
t = 15 / 2.5
t = 6 seconds
Therefore, the length of time the box slides from stopping is 6 seconds.
b) To find the time it takes to slide 10.0 meters, we need to determine the time (t) using the same equation:
s = ut + (1/2)at^2
Rearranging:
t = sqrt((2s) / a)
Plug in the known values:
t = sqrt((2 * 10) / (-2.5))
Simplifying:
t = sqrt(-8 / (-2.5))
t = sqrt(3.2)
t ≈ 1.7889 seconds
Therefore, the time it takes to slide 10.0 meters is approximately 1.7889 seconds.