46 c,

`Deltat` = 15 s

`Deltav` = `v_2-v_1` = 90-60 = 30 `(km)/h` = `8.dot(3)` `m/s`

a = `(Deltav)/(Deltat)` = `8.dot(3)/15` = `0.dot(5)` `m/s^2`


47,

a,

v = 225 `(km)/h` = 62,5 `m/s`

t = 20 s

a = `v/t` = `62.5/20` = 3,125 `m/s^2`.

b,

s = `a/2*t^2` = `3.125/2*20^2` = 625 m


51,

- 1 s alatt megtesz:

`s_1` = `a/2*t_1^2` = `5/2*1^2` = 2,5 m

- A 2. másodperc azt jelenti hogy 2 másodperc alatt - 1 másodperc alatt:

`s_2` = `a/2*t_2^2` = `5/2*2^2` = 10 m

`Deltas_2` = `s_2-s_1` = 10-2,5 = 7,5 m

- 3. másodpercben: 3 másodperc alatt - 2 másodperc alatt:

`s_3` = `a/2*t_3^2` = `5/2*3^2` = 22,5 m

`Deltas_3` = `s_3-s_2` = 22,5-10 = 12,5 m

- 4. másodperc: 4 másodperc alatt - 3 másodperc alatt:

`s_4` = `a/2*t_4^2` = `5/2*4^2` = 40 m

`Deltas_4` = `s_4-s_3` = 40-22,5 = 17,5 m

Az arányok:

2,5:7,5:12,5:17,5. Osztod mindet az elsővel:

1:3:5:7

`v_2` = `a*t_2` = `5*2` = 10 `m/s`

`v_4` = `a_t_4` = `5*4` = 20 `m/s`

`Deltav_(2-4)` = `v_4-v_2` = 20-10 = 10 `m/s`


52,

v = `v_0+a*t`

s = `v_0*t+a/2*t^2`

Behelyettesítve az ismert értékeket:

I. 12.8 = `v_0+a*4`

II. 50 = `v_0*4+a/2*4^2` = `4*v_0+8*a`

2*I.: `2*v_0+8*a`

II. - 2*I.:

`2*v_0` = `50-2*12.8` = 24,4

`v_0` = 12,2 `m/s`

I. : 12.8 = `12.2+4*a`

0.6 = 4a

a = 0,15 `m/s^2`.


53.

`v_1` = 54 `(km)/h` = 15 `m/s`

`Deltav` = `v_2-v_1` = 72-54 = 18 `(km)/h` = 5 `m/s`

a = 2,5 `m/s^2`

t = `v/a` = `5/2.5` = 2 s

s = `v_1*t+a/2*t^2` = `15*2+2.5/2*2^2` = 30+5 = 35 m


54,

`Deltav` = `v_2-v_1` = 4-2 = 2 `m/s`

a = 10 `m/s^2`

t = `(Deltav)/a` = `2/10` = 0,2 s

s = `v_1*t+a/2*t^2` = `2*0.2+10/2*0.2^2` = 0.4+0.2 = 0,6 m.