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.
a)the time it takes to slide the last 10.0 meters
average speed is ... (15 m/s) / 2 = 7.5 m/s
it takes 6 s to stop ... (45 m) / (7.5 m/s)
the acceleration is ... (15 m/s) / (6 s) = 2.5 m/s^2
for the same acceleration
... stopping from 10.0 m takes the same amount of time as
... starting and going 10.0 m
10.0 = 1/2 * 2.5 * t^2
To find the time it takes for the box of lollipops to slide the last 10.0 meters, we can use the equations of motion.
First, we need to determine the acceleration of the box. Since the box comes to rest, we know that its final velocity is 0 m/s.
Using the equation:
v^2 = u^2 + 2as,
where:
- v is the final velocity (0 m/s),
- u is the initial velocity (15 m/s),
- a is the acceleration,
- s is the displacement (45 m - 10 m = 35 m),
we can rearrange the equation to solve for the acceleration:
a = (v^2 - u^2) / (2s).
Plugging in the values, we get:
a = (0^2 - 15^2) / (2 * 35) = -225 / 70 ≈ -3.21 m/s^2 (rounded to two decimal places).
Now that we know the acceleration, we can use the equation:
v = u + at,
where:
- v is the final velocity (0 m/s),
- u is the initial velocity (15 m/s),
- a is the acceleration (-3.21 m/s^2),
- t is the time.
Rearranging the equation to solve for time:
t = (v - u) / a.
Plugging in the values, we get:
t = (0 - 15) / (-3.21) ≈ 4.67 seconds (rounded to two decimal places).
Therefore, it takes approximately 4.67 seconds for the box of lollipops to slide the last 10.0 meters.