Motion Test - 2

We know that acceleration is negative when distance is negative, i.e. distance decreases with time.
In the graph, distance of only one interval decreases with time, which is BC.

Area of field = 1 hectare = 0.01 sq. km

Side of field = 0.1 km

Total distance covered by boy = 0.1*4 = 0.4 km

Speed of boy = 10 km/hr

Time taken = distance/speed

= 0.4/10 = 0.04 hr = 0.04*60 = 2.4 minutes

Length of battalion (L) = 250 m
Speed (s) = 50 paces/min = 37.5/60 m/s (1 pace = 75 cm = 0.75 m)
(50 paces = 50*0.75 = 37.5 m)
Time (t) = 1hr = 3600 sec
s = (250+L)/t
37.5/60 = (250+L)/3600
Solving this, we get
\'L\' = 2000 m = 2 km

In first 2 minutes, height reached after slipping = 4-2 = 2 m
In 4 minutes, height reached after slipping = 4 m
//ly, in 116 minutes, height reached after slipping = 116 m
Now, in the next minute, monkey ascends 4 m and reaches the top.
Hence, total time taken = 117 minutes

Time taken to reach surface (t) = ?
Dropping height = 125 m
Initial velocity (u) = 0 m/s (body is at rest initially)
We know that,
s = ut + 1/2gt²
125 = 0+ 1/2*9.8*t²
Solving for t, we get
t = 5.05 sec = 5 sec approx

Time taken to reach surface (t) = 5s
Velocity with which it strikes the surface (v) = ?
Initial velocity (u) = 0 (body is at rest initially)
We know that,
v = u + gt
v = 0 + 9.8*5
v = 49 m/s