Q10DQ - University Physics with Modern Physics

Question

Does a car’s kinetic energy change more when the car speeds up from 10 to 15 m/s or from 15 to 20 m/s? Explain.

Step-by-Step Solution

Answer

Yes, the kinetic energy changes more when the car speeds up.

Step 1: Describe the Kinetic Energy

The expression for the Kinetic Energy is given by,

$\mathit{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$ 

Here, mis the mass of an object, and v is the velocity of the object.

Step 2: Determine whether the kinetic energy change more when the car speeds up from 10 to 15 m/s or from 15 to 20 m/s

Find the change in kinetic energy when speed changes from ${\mathrm{v}}_1=10\mathrm{m}/\mathrm{s}$ to ${\mathrm{v}}_2=15\hspace{0.33em}\mathrm{m}/\mathrm{s}$.

$$\begin{gathered} ∆K=\frac{1}{2}m\left(v_2^2-v_1^2\right) \\ =\frac{1}{2}m\left({15}^2-{10}^2\right) \\ =62.5m \end{gathered}$$ 

 

Find the change in kinetic energy when speed changes from ${\mathrm{v}}_1=15 \mathrm{m}/\mathrm{s}$ to ${\mathrm{v}}_2=20\mathrm{m}/\mathrm{s}$.

$$\begin{gathered} ∆K=\frac{1}{2}m\left(v_2^2-v_1^2\right) \\ =\frac{1}{2}m\left({20}^2-{15}^2\right) \\ =87.5m \end{gathered}$$

 

From the above calculations, it is clear that the change is kinetic energy in second condition is more than the first condition.

 

Therefore, yes, the kinetic energy changes more when the car speeds up from 10 to 15 m/s or from 15 to 20 m/s.