1(a)
Step 1: Convert speed to m/s.
v=54×185=15 m/s
Step 2: Distance to cross the pole = length of train = 150 m.
Step 3: Time taken =speeddistance.
t=15 m/s150 m=10 s
10 s
1(b)
Step 1: Convert speeds to m/s.
Train 1: v1=54×185=15 m/s
Train 2: v2=36×185=10 m/s
Step 2: Relative speed (opposite direction) =v1+v2=15+10=25 m/s.
Step 3: Distance to cross =150 m+200 m=350 m.
Step 4: Time taken =25 m/s350 m=14 s.
14 s
1(c)
Step 1: Convert speeds to m/s.
Train 1: v1=15 m/s
Train 2: v2=18×185=5 m/s
Step 2: Relative speed (same direction) =v1−v2=15−5=10 m/s.
Step 3: Distance to cross =150 m+250 m=400 m.
Step 4: Time taken =10 m/s400 m=40 s.
40 s
2(a)
Step 1: Outward speed a=40 km/h, return speed b=60 km/h.
Step 2: Average speed for equal distances =a+b2ab.
40+602×40×60=1004800=48 km/h
48 km/h
2(b)
Step 1: Outward: 40 km at 50 km/h.
Time =5040=0.8 h.
Step 2: Return: 60 km at 40 km/h.
Time =4060=1.5 h.
Step 3: Total distance =40+60=100 km.
Total time =0.8+1.5=2.3 h.
Step 4: Average speed =2.3100=2310000≈43.48 km/h.
\dfrac{10000{23} km/h}
3(a)
Step 1: Initial speed u=72×185=20 m/s.
Final speed v=0 m/s, a=−10 m/s2.
Step 2: Stopping distance from v2=u2+2as.
0=(20)2+2(−10)s
400=20s
s=20400=20 m
20 m
3(b)
Step 1: Initial speed u=0 m/s, a=2 m/s2, t=10 s.
Step 2: Distance s=ut+21at2.
s=0+21×2×(10)2=100 m
100 m
3(c)
Step 1: Let length of train =L m, speed =v m/s.
Time to pass man (point): vL=18 s ⇒L=18v.
Step 2: Time to pass 100 m platform: vL+100=30 s.
Step 3: Subtract equations: v100=12 s ⇒v=12100 m/s.
Step 4: L=18×12100=150 m.
150 m, \dfrac{100{12} m/s}
3(d)
Step 1: u=20 m/s upward, g=10 m/s2.
Max height h=2gu2.
h=2×10(20)2=20400=20 m
20 m