1. SchoolDD.com
2
www.schoolDD.com

2. 2
F F
F F FF F F
F F F F
F F F
F F F F F F
F F F F F F
F F F F F
F F F F
2.1 F
F F F F F
F F
1. F F F
F
F F F 1 2 F 1+2=3
1 . 2 . 3 .
+ =
2. F F F
FF F 2.2
F F F F F
F F
FA 5 F
5 .
– F F www.schoolDD.com 1

3. F F F 3 4 F
F 5 ( F F 3+4)
5N
4N
3N
F
- F F F F F F FF
F F
2.2 - F
F F F F F
F F F F F F
F F F F FF F F
F F F F F
F F F F
F F F F F 3 F F
F F FF F F F F
F F
F F =
– F F www.schoolDD.com 2

4. F F
F F F F F F F
R=
R= F F
=
A= F
B= F
= F F
F
F
.
2 3
-
= + = -
2+3=5 3-2=1
.
= +
3 3
=
2
2
F
- F F F F
- . F F F F F F F
F - F
F F F ( - = + (- ))
- F F . F F F
F F , , , F F F F F
– F F www.schoolDD.com 3

5. = ? , = ?
( ) + ( )=( )+( )?
2.3
F F F
F F F F
F
s1, t1
s1
s2, t2
“ F
s2
F F
s3, t3
s3 F F ”
F F F F F 3 F s1 , s2 s3 FF
F s1, s2 s3
F s2
1. s F F
F F F F F (m)
2. F
F F (m)
F
3. v F F F F
F (m/s)
v=
F 2
1. vt F F F
– F F www.schoolDD.com 4

6. F
vt = F
= ,
2. vav F F F
vav =
F
4. F F F F
F F (m/s)
=
F 2
1. t F F
F
t = F F
2. av FF F
F
F
av = F F
5. F F F
2
F F (m/s2 )
=
F F 2
1. F t F
F . F F
– F F www.schoolDD.com 5

7. F
t = F
2. F av F
F
av =
F
- F a= = v2 > v 1 F F F F
v2 < v 1 F F F ...
(v2 > v1) a +
(v2 < v1) a -( F F )
(v2 = v1) a 0
F
F F +, - 0
F F F ( F -)
F F F ?
F F F 0.5 m/s F F F
F F F ?
F 1
A C F B
C
50 m s = AB + BC
30 m = 40 + 30
A B = 70 m Ans
40 m = AC
= 50 m A C Ans
F F F
– F F www.schoolDD.com 6

8. F 2
P Q F 10
.
.
P 140 m Q .
.
. P
F 20
F
F s
π
. = = x = 220 m. Ans
. = PQ = 140 m. P Q Ans
. vav = = = 22 m/s Ans
. av = = = 14 m/s P Q Ans
. av = = = 0 m/s Ans
F 3
F F 4 m/s F 80 m. F F 10 m/s
F 50 m.
F F F
vav = ?
v1 = 4 m/s v2= 10 m/s
av = ?
s1 = 80 m s2 = 50 m
v = 4 m/s v =4
F F F F vav = s /t s = s1 + s2 t F F F F F
– F F www.schoolDD.com 7

9. v = F t =
t1 = = = 20 s
t2 = = = 5s
vav = = = = = 5.20 m/s Ans
av = F
= = = 5.20 m/s Ans
F F FF F F
F
F 4
F 3 F F F F
v1 = 4 m/s vav = ?
v2= 10 m/s av = ?
s1 = 80 m
v =s24 =m/s m
50
v =4
vav = = = = = 5.20 m/s
vav = 5.20 m/s F F F Ans
F av = F
av = = = 2.0 m/s F F F
F F F Ans
F
- F F F F F
F F F F F F FF
FFF F F F
– F F www.schoolDD.com 8

10. 2.4
F F F
F
t0 t1 t2 t3 t4 t5 t6
••• • • • • • •
s1
s2
s3
s4
s5
s6
50 F F F 1/50
F t0 - t2 v0 2 = = t1
F t1 - t5 v1 5 =
t3 v3 =
F F t2 - t5 a2 5 =
F t3 a3 = = F F t2 t4
50 F 100 F F F F
F ?
F F F ?
– F F www.schoolDD.com 9

11. F 5
F F F 4/50
F s1 = 1.0 cm , s2 = 2.2 cm , s3 = 3.6 cm , s444 = 5.2 cm , s5 = 7.0 cm s6 = 9.0 cm
50 F
F t = F
F
a4 = -------(1)
v3 = = (5.2 - 2.2) x 10-2 )/( ) = 0.75 m/s
v5 = = (9.0 - 5.2) x 10-2 )/( ) = 0.95 m/s
F v3 v5 (1)
F a4 =
=
a4 = 5 m/s2 Ans
F
F
• • • • • • - ( )
-
F
- F F
F
•• • • • • - ( ) F
-
F
- F ( +)
F
• • • • • • - ( ) F
-
F
- F ( -)
– F F www.schoolDD.com 10

12. 2.5 F F () () F () (t)
F F F F F F
F F F F
F F FF F F F F F
F F F F F F F F F
y
y = mx + c
y
c x
x
F y = mx + c
m (Slope) F F
c y
() (t)
= =
= t
y = mx + c F
F () (t) F (slope) F ()
F 0 (c = 0)
= t
→ → F =0
t
3
→ → F ( +)
2
1 t
– F F www.schoolDD.com 11

13. 3
2
→ → F ( -)
1
t
() (t)
F = =
= t
y = mx + c F
F () (t) F (slope) F F ()
= t
→ F
.= F .t =
t
F
- F F F
F F F y = mx + c F
F y,m,x F y x
m F
- F F
F F F F F F F F F
F F F
F F F F F F F
– F F www.schoolDD.com 12

14. F 6
(m)
. 50
20 . 50
. 5 , 20 35
0 t (s)
10 20 30 40 50 . 50
-10 . 50
. (s)
F F F F
t = 45 t=0 t = 10 → 30 +
F F t=0
s1 = 20
F 10 F 20 m F t = 10-30
s3 = 10 s2 = 20 F 20 m F F t = 30-40
t = 40 F F F F t
s4 = 10 = 40 F F F F F
t = 50
F F t = 45 F
- + -10 m F F F t = 50
=0( F F )
s = s1 + s2 + s3 + s4 ( F )
= 20 + 20 + 10 + 10 = 60 m Ans
. () 50
=0 F F F ( F ) Ans
. 5 , 20 35
t F t
( = = t y = mx + c F = m)
t=5s = (20 - 0)/(10 - 0) = 2 m/s Ans
t = 20 s = 0 m/s Ans
t = 35 s = (0 - 20)/(40 - 30) = -2 m/s ( F ) Ans
– F F www.schoolDD.com 13

15. . (vav)
F
=
F
vav =
vav = = 1.2 m./s Ans
. ( av)
F
=
F
av = F
= 0 m/s Ans
F 7
F () (t) F
(m/s)
. F
. F
20 .
15
s3 .
s2 s4
t (s) . F 1 7
0 s1 2 4 6 8
-15
t=2 s t=0
1
s2 s3 s4 F
t=4 t=6 t=8
. F s
F F F F F
s= F ( F )
F F F F
s = s1 + s2 + s3 +s4
= (½ x 2 x 15) + (½ x 2 x 15) + (½ x (20 + 15) x 2) + (½ x 2 x 20)
– F F www.schoolDD.com 14

16. s = 85 m Ans
. F
= F t( )
= s1 + s2 + s3 + s4
= - 15 + 15 + 35 + 20
= 55 m Ans
. vav
vav =
=
vav = 10.62 m/s Ans
. av
av = F
av =
av = 6.8 m/s Ans
. F 1 7 1 , 7
F = t( = )
∆
∆
= (0 (-15))/(2-0) = 7.5 m/s2 Ans
∆
t = 1s = 1 =
∆
∆
t = 7s = 7 =
∆
= (0 20)/(8-6) = -10 m/s Ans
2.6 F F a
F F F
F F F F F F F F F F F
F F F
F F F F F F
u t v
s
– F F www.schoolDD.com 15

17. F u / F t
v / F s
F
F a= =
F at = v u v = u + at ---(1)
v F v t F F
v = at + u v = u + at
v
v = at + u
u
y = mx + c
t
t
. F v t s s= ---(2)
F v = u + at (2)
F s=
s = ut + ½ at2 ---(3)
F t= (2)
F s=
2as = v2 u2
v2 = u2 + 2as ---(4)
4
u a( )
v
1. v = u + at
t
2. s = t
3. s = ut + ½ at2 s
4. v2 = u2 + 2as
F FF
F F t
t = F t=0
u = F
v =
s = F
a = F F ( + v>u - v<u F )
F F F F s = vt
– F F www.schoolDD.com 16

18. F FF F = F
F F F F s,u,v,a
F 8
F F 2 m/s2 F 5
F F F
a = 2 m/s2 F F F F
u=0 v=? F F F F F F F F F F
t = 5s F F FF F F ? F
F a = 2, t = 5, u = 0
s=? F F F F v = ?, s
=? F F 4 F F
Fu,a,t v F v = u + at
v = 0 + 2x5
v = 10 m/s Ans
s F s = t
s = (0 + 10 )/2 x 5
s = 25 m Ans
s = ut + ½ at2
s = 0 + ½ x 2 x 52
s = 25 m/s Ans
v2 = u2 + 2as
102 = 0 + 2(2) s
s = 25 m Ans
– F F www.schoolDD.com 17

19. F
- F F F s F 2,3 4 F F
4 ( F F) F F
F F F F F F F F FFF F
F F F F
F 9
F F F 72 / F F
F 5 F F
a= ? F F F F F
u = 20 m/s v= 0 F F F FF F F
t= 5 s F F F F
F F F
s= ?
F F
F F F F F / F
2
/ F F
u = 72 km/hr = (72 x 103m)/(60 x 60 ) m/s
u = 20 m/s
Fu,v t a F v = u + at
F F F
0 = 20 + a(5)
F F
∴ a = -4.0 m/s2 Ans u = 20 v=0
Fu,v t s F s = t
= (20 + 0)/2 (5)
∴ s = 50 m Ans
– F F www.schoolDD.com 18

20. F 10
A B F F F B F A F
F 4 m/s2 6 m/s2 A F 100 m. F F F
F F
F F F
u=0 aA = 4
A
A tA
sB - sA = ? sA = 100
u=0 aB = 6 B
B
tB
sB
∴ F F tA = tB = t
t F A
s = ut + ½ at2
100 = 0 + ½ x 4 x t2
t2 = 50
t =5 s
B F sB
s = ut + ½ at2
sB = 0 + ½ x 6 x 50
sB = 150 m
∴ F F F
sB - sA = 150 - 100 = 50 m Ans
F
- F F F F F F !
– F F www.schoolDD.com 19

21. F 11
F F 150 5 F F
F F 5 F 100 F F
F F F
a1 = ? v a2 = 0
u= ? v
t1 = 5 t2 = 5
s1 = 150 s2 = 100
F
v s = vt v = s/t ( v , a2 = 0)
v = 100/5 = 20 m/s
F
F u s = t
F F 150 = (u + 20)/2 (5)
u = 40 m/s Ans
F a1 v = u + at
F F 20 = 40 + a1(5)
a1 = - 4 m/s2 Ans ( F )
2.7 F F F F
F F F F F
F F F F F F g
F 9.8 m/s2 F F FF F
F F F F F
F F F F F F
F F F
4 F 2.6 F F F F F a F F F F g
– F F www.schoolDD.com 20

22. v=0 F F 4
F a g = 9.8 m/s2 ( F
+u +s +u 10 m/s ) 2
g F F FF
+s
-s -g
+g F / F
-v F .. F
+v
F u F
u F
F F
F 12
F 80
. F F F
. F
. F t
F
Fs,u a t F s = ut + ½ at2
u =0 F F F 80 = 0 + ½ x 10 x t2
t2 = 16
s = 80 t =? a =g
80 t = 4.0 s Ans
v =?
v
F u,a t v F v = u + at
F F v = 0 + 10 x 4
v = 40 m/s Ans
– F F www.schoolDD.com 21

23. F 13
F F 60 F 20 m/s
. F F F
. F F
. F 1,2,4,5
.
v=0
+s +u = 20 m/s
F F F
-s
a=g
s = 60
. F t
Fs,u a t F s = ut + ½ at2
F F -60 = 20 t + ½ (-10) t2 (s a F u)
t2 - 4 t - 12 = 0
(t - 6)(t + 2) = 0
t = 6 , -2 ( F F F )
F
t = 6 s Ans
. smax
v=0
Fu,v a s F v2 = u2 + 2as
F F 0 = 202 + 2 (-10) smax (a F u)
smax = 20 m (s u) Ans
. F t = 1,2,4,5 s
Fu,t a F s s = ut + ½ at2
v = u + at
t = 1s
s = ut + ½ at2
– F F www.schoolDD.com 22

24. 2
s = 20(1) + ½ (-10) (1)
s = 15 m (s u F ) Ans
v = u + at
v = 20 + (-10) (1)
v = 10 m/s (v u) Ans
t =2s
s = ut + ½ at2
s = 20(2) + ½ (-10)(1)2
s = 20 m Ans
v = u + at
v = 20 + (-10) (2)
v = 0 m/s Ans
t = 4s
s = ut + ½ at2
s = 20(4) + ½ (-10)(4)2
s = 0 m F Ans
v = u + at
v = 20 + (-10) (4)
v = -20 m/s ( F u=v F F ) Ans
t = 5s
s = ut + ½ at2
s = 20(5) + ½ (-10) (5)2
s = -25 m F (s F u F F ) Ans
v = u + at
v = 20 + (-10) (5)
v = -30 m/s Ans
– F F www.schoolDD.com 23

25. .
F F t = 6s( )
v = u + at
v = 20 + (-10) (6)
v = -40 m/s Ans
4 a F ?
4 u,v,a s + , -?
F F F
F
F F
F F F ?
F
- F F F F F F F F
F
F
– F F www.schoolDD.com 24

26. 2.8 F
F F F F F F 0.5
F F F F F F F
F F F F F F
F F F F F
F F
F F
FF
F F
- F ( F )
- ( ) F
- F F F ( )
F
F = + (- F )
F 14
FA F 30 / FB F 40 /
F FB F FA
vA = 30 m/s -v F = -vA
m/s
v = vB
v
vB = 40 m/s
F
F
v F =
v F =
v F = 50 m/s
F FA FB F 50 m/s F Ans
F F F F
F
F F F F
– F F www.schoolDD.com 25