A car of mass 2000 kg is initially moving at 18 km h-1. How much is the force required to change the speed to 36 km h-1 in 2 s?

1. Break Down the Problem

To find the force required to change the speed of the car, we need to:

1. Convert the initial and final speeds from km/h to m/s.
2. Calculate the change in speed (acceleration).
3. Use Newton's second law ($F = ma$) to find the force.

2. Relevant Concepts

• Newton's Second Law: $F = ma$
• Acceleration: $a = \frac{\Delta v}{\Delta t}$
• Conversion from km/h to m/s: $1 \text{ km/h} = \frac{1}{3.6} \text{ m/s}$

3. Analysis and Detail

1. Convert speeds:

   • Initial speed: $v_i = 18 \text{ km/h} = \frac{18}{3.6} = 5 \text{ m/s}$
   • Final speed: $v_f = 36 \text{ km/h} = \frac{36}{3.6} = 10 \text{ m/s}$

2. Calculate acceleration:

   • Change in speed ($\Delta v$): $\Delta v = v_f - v_i = 10 \text{ m/s} - 5 \text{ m/s} = 5 \text{ m/s}$
   • Time ($\Delta t$) = 2 s
   • Acceleration ($a$): $a = \frac{\Delta v}{\Delta t} = \frac{5 \text{ m/s}}{2 \text{ s}} = 2.5 \text{ m/s}^2$

3. Calculate force:

   • Mass ($m$) = 2000 kg
   • Force ($F$): $F = ma = 2000 \text{ kg} \times 2.5 \text{ m/s}^2 = 5000 \text{ N}$

4. Verify and Summarize

The calculations have been verified and show that the acceleration is correctly computed, leading to the force needed to change the speed as required.

Final Answer

The force required to change the speed of the car to 36 km/h in 2 seconds is 5000 N.