A box accidentally falls from the back of a truck and hits the groud with a speed of 15m/s forward. It slides along the groud with uniform acceleration for a distance of 45m before coming to rest. Determine the time it takes to slide the last 10m.
To determine the time it takes for the box to slide the last 10m, we need to first find the acceleration of the box.
Given:
Initial velocity (u) = 15 m/s (forward)
Distance traveled (s) = 45m
Final velocity (v) = 0 m/s (comes to rest)
We can use the equation of motion: 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,
and s is the distance traveled (45m).
Plugging in the values, the equation becomes:
0^2 = 15^2 + 2a(45).
Simplifying the equation, we get:
225 = 90a.
Dividing both sides by 90, we find:
a = 225 / 90 = 2.5 m/s^2.
Now that we have the acceleration, we can use the equation of motion: v = u + at, where:
v is the final velocity (0 m/s),
u is the initial velocity (15 m/s),
a is the acceleration (2.5 m/s^2),
and t is the time we want to find.
Plugging in the values, the equation becomes:
0 = 15 + 2.5t.
Subtracting 15 from both sides, we get:
-15 = 2.5t.
Dividing both sides by 2.5, we find:
t = -15 / 2.5 = -6 seconds.
Since time cannot be negative, we discard this solution, which means the box takes more than 6 seconds to slide the last 10m. However, without knowing the exact time it takes to slide the first 35m, we cannot determine the time for the last 10m.