Question

An automobile engine propels a $1000kg$car (A) along a levelled road at a speed of $36km{h}^{-1}$. Find the power if the opposing frictional force is $100N$. Now, suppose after travelling a distance of$200m$, this car collides with another stationary car (B) of same mass and comes to rest. Let its engine also stop at the same time. Now car (B) starts moving on the same level road without getting its engine started. Find the speed of the car (B) just after the collision.

Answer 1

Step 1: Given data

Mass of the car A, $m_A=1000kg$

Initial speed of the car A, $u_A=36km{h}^{-1}=36\times \frac{5}{18}=10m{s}^{-1}$

$m_A=m_B=1000kg$

Frictional force, $F=100N$

Step 2: Calculating the power

Car A moves with a uniform speed, which means the engine of the car applies a force equal to the frictional force.

$Power\left(P\right)=Force\left(F\right)\times velocity\left(v\right)$

$P=100N\times 10m{s}^{-1}=1000W$

Step 3: Calculating the velocity of car B

After collision,

$m_A\times u_A+m_B\times u_B=m_A\times v_A+m_B\times v_B$

$\Rightarrow 1000\times 10+1000\times 0=1000\times 0+1000\times v_B$

$\Rightarrow v_B=10m{s}^{-1}$

Hence, the velocity of car B is$10m{s}^{-1}$ .