Question

Find the average frictional force needed to stop a car weighing 500kg in a distance of 25m, if the initial speed is 72km/hr.

Answer 1

Hint:In this question, use the concept of the equation of motion that is use the third equation of motion to calculate the acceleration of the car. The final speed of the car will be zero as the car comes to rest. Calculate the initial speed of the car and then the acceleration of the car. Substitute the values of acceleration and mass to obtain the force.

Complete step by step answer:
In the question, We are given the mass of the car \[\left( {\text{m}} \right)\] is \[50{\text{0}}\;{\text{kg}}\], the initial speed \[\left( u \right)\] of the car is \[72\;{\text{km/h}}\] the final speed of the car is zero that is \[v = 0\], and the total stopping distance covered by the car $\left( s \right)$ is \[25\;{\text{m}}\].

First we convert the initial speed of the car from ${\text{km/h}}$ to ${\text{m/s}}$ as,
\[u = 72 \times \dfrac{{1000}}{{3600}}\;{\text{m/s}}\]
After calculation we get,
\[ \Rightarrow u = 20\;{\text{m/s}}\]

Now, we calculate the acceleration of car by the using equation of motion
\[{v^2} - {u^2} = 2as\]
Now, we substitute the values in the above equation,
\[{0^2} - {20^2} = 2 \times a \times 25\]
After calculation we get,
\[a = - 8\;{\text{m/}}{{\text{s}}^{\text{2}}}\]

As we know that, here the negative sign indicates that the acceleration is in the opposite direction.
Now, we will calculate the average frictional force for the car, using the formula,
\[F = m \times a\]

Where, \[F\] is the frictional force \[m\]is the mass of the car, and \[a\] is the acceleration of the car.

Substitute the values in the above equation we get,
\[ \Rightarrow F = 500 \times 8\]

After multiplication we get,
\[\therefore F = 4000\;{\text{N}}\]
Therefore, the frictional force is required to stop a car weighing \[500\;{\text{kg}}\] is \[4000\;{\text{N}}\].

Note:As we know that if the acceleration is in negative sign means an opposite force is applied on the body to accelerate the body and the acceleration is positive then external force is applied on the body in the direction of the motion to accelerate the body.