Questions: Automobil se giba jednoliko ubrzano iz mirovanja i kad prijeđe 100 m, postigne brzinu 10 ms¹. Kolika će mu biti brzina nakon što prijeđe 400 m? a) 20 m s⁻¹ c) 40 m s⁻¹ b) 30 m s⁻¹ d) 80 m s¹

Automobil se giba jednoliko ubrzano iz mirovanja i kad prijeđe 100 m, postigne brzinu 10 ms¹. Kolika će mu biti brzina nakon što prijeđe 400 m?
a) 20 m s⁻¹
c) 40 m s⁻¹
b) 30 m s⁻¹
d) 80 m s¹

Transcript text: Automobil se giba jednoliko ubrzano iz mirovanja i kad prijeđe 100 m , postigne brzinu $10 \mathrm{~ms}^{\text {¹.}}$. Kolika će mu biti brzina nakon što prijeđe 400 m ? a) $20 \mathrm{~m} \mathrm{~s}^{-1}$ c) $40 \mathrm{~m} \mathrm{~s}^{-1}$ b) $30 \mathrm{~m} \mathrm{~s}^{-1}$ d) $80 \mathrm{~m} \mathrm{~s}^{1}$

Solution

Solution Steps

Step 1: Understand the Problem

The problem involves an automobile moving with uniform acceleration from rest. We are given that after traveling 100 meters, the automobile reaches a speed of $10 \, \text{m/s}$. We need to find the speed of the automobile after it has traveled 400 meters.

Step 2: Use the Kinematic Equation

We will use the kinematic equation that relates initial velocity ($v_0$), final velocity ($v$), acceleration ($a$), and distance ($s$):

\[ v^2 = v_0^2 + 2as \]

Since the automobile starts from rest, $v_0 = 0$.

Step 3: Calculate the Acceleration

First, calculate the acceleration using the information that after 100 meters, the speed is $10 \, \text{m/s}$:

\[ 10^2 = 0 + 2a \times 100 \]

\[ 100 = 200a \]

\[ a = \frac{100}{200} = 0.5 \, \text{m/s}^2 \]

Step 4: Calculate the Final Velocity After 400 Meters

Now, use the same kinematic equation to find the velocity after 400 meters:

\[ v^2 = 0 + 2 \times 0.5 \times 400 \]