At highway speeds, a particular automobile is capable of an acceleration of about 1.8 m/s2
At this rate, how long does it take to accelerate from 75 km/hkm/h to 100 km/hkm/h ?

To solve this problem, we need to find the time it takes for the automobile to accelerate from 75 km/h to 100 km/h given an acceleration of 1.8 m/s².

### Step 1: Convert speeds from km/h to m/s
We need to convert the initial and final speeds from km/h to m/s since the acceleration is given in m/s².

- Initial speed \( v_i = 75 \, \text{km/h} \)
- Final speed \( v_f = 100 \, \text{km/h} \)

To convert from km/h to m/s:
\[
\text{Speed (m/s)} = \text{Speed (km/h)} \times \frac{1000 \, \text{m/km}}{3600 \, \text{s/h}} = \text{Speed (km/h)} \times \frac{5}{18}
\]

- Initial speed:
\[
v_i = 75 \times \frac{5}{18} = 20.83 \, \text{m/s}
\]
- Final speed:
\[
v_f = 100 \times \frac{5}{18} = 27.78 \, \text{m/s}
\]

### Step 2: Use the kinematic equation
We can use the kinematic equation that relates acceleration, initial velocity, final velocity, and time:
\[
v_f = v_i + at
\]
Where:
- \( v_f = 27.78 \, \text{m/s} \)
- \( v_i = 20.83 \, \text{m/s} \)
- \( a = 1.8 \, \text{m/s}^2 \)

Rearranging the equation to solve for time \( t \):
\[
t = \frac{v_f - v_i}{a}
\]

### Step 3: Calculate the time
\[
t = \frac{27.78 \, \text{m/s} - 20.83 \, \text{m/s}}{1.8 \, \text{m/s}^2}
\]
\[
t \approx \frac{6.95 \, \text{m/s}}{1.8 \, \text{m/s}^2} \approx 3.86 \, \text{seconds}
\]

### Final Answer
It takes approximately **3.86 seconds** to accelerate from 75 km/h to 100 km/h.

Would you like more details or have any other questions?

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Here are 5 related questions to explore:
1. How much distance is covered during the acceleration?
2. What would the time be if the acceleration were doubled?
3. How does the acceleration compare to other typical vehicles?
4. What is the force required to produce this acceleration if the car's mass is 1500 kg?
5. How would the acceleration time change if the initial speed were 50 km/h instead?

**Tip:** Always double-check unit conversions in physics problems to avoid mistakes.

At highway speeds, a particular automobile is capable of an acceleration of about 1.8 m/s². At this rate, how long does it take to accelerate from 75 km/h to 100 km/h?

Find out how to calculate the time required for a car to accelerate from 75 km/h to 100 km/h with a given acceleration of 1.8 m/s². This problem involves key kinematic concepts, unit conversion, and linear acceleration. Ideal for students in Grades 9-12.

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