Question

What is the work to be done to increase the velocity of a car from $30km{h}^{-1}to60km{h}^{-1}$ if the mass of car is $1500kg$?

Answer 1

Step 1: Given Data

Initial velocity $\left(v_i\right)=30km{h}^{-1}$

Final velocity $\left(v_f\right)=60km{h}^{-1}$

Mass (m) $=1500kg$

Step 2: Formula used

According to Work - Energy Theorem,

Work (W) = Change in Kinetic Energy

$W=\frac{1}{2}m{v_f}^2-\frac{1}{2}m{v_i}^2$

Step 3: Converting initial and final velocities to the SI unit

$$\begin{gathered} 30km{h}^{-1}=30x\frac{1000m}{3600s}=30x\frac{5}{18}=\frac{25}{3}m{s}^{-1} \\ 60km{h}^{-1}=60x\frac{1000m}{3600s}=60x\frac{5}{18}=\frac{50}{3}m{s}^{-1} \end{gathered}$$

Step 4: Calculating work

$$\begin{gathered} W=\frac{1}{2}m{v_f}^2-\frac{1}{2}m{v_i}^2 \\ W=\frac{m}{2}({v_f}^2-{v_i}^2) \\ W=\frac{1500}{2}[{\left(\frac{50}{3}\right)}^2-{\left(\frac{25}{3}\right)}^2]W=750(\frac{2500}{9}-\frac{625}{9}) \\ W=750x\frac{1875}{9} \\ W=156250J \end{gathered}$$

Hence, the work done to increase the velocity of the car is $156250J$