Question

Gogi was driving at $20m/s$. He applied brakes which generated force equal to $500N.$ Find the distance after which the car will stop if its mass is $100kg.$

Answer 1

Hint: First note down all the given terms and unknown terms. Find the correlation between the known terms and find the unknown values. Here we will use equations of the force and different equations of Newton’s laws of motion. Substitute the values and simplify accordingly.

Complete step by step answer:
Given that: Gogi was driving at $20m/s$
The initial velocity, $u = 20m/s$
The Final velocity, $V = 0m/s$ (Since car comes at rest when brake is applied)
Applied Force, $F = 500N$
Mass of the car, $m = 100kg$
Now, first use the formula of Force which will give us the unknown acceleration.
$F = m \cdot a$
Place the unknown values in the above equation
$500 = 100 \cdot a$
Now, simplify and make the unknown acceleration “a” as the subject –
$
\Rightarrow a = \dfrac{{500}}{{100}} \\
\Rightarrow a = 5m/{s^2} \\
$
Use, the Newton’s equation of motion –
$a = \left( {\dfrac{{v - u}}{2}} \right)t$
Place the known values in the above equation
$5 = \left( {\dfrac{{0 - 20}}{2}} \right)t$
Simplify and make “t” the subject –
$
\Rightarrow t = \dfrac{{10}}{{ - 20}} \\
\Rightarrow t = - 0.5s \\
$
Since time can never be negative
$t = 0.5s$
Lastly, use distance travelled using Newton’s equation of motion –
$s = \left( {\dfrac{{v + u}}{2}} \right)t$
Put the known values
$
\Rightarrow s = \left( {\dfrac{{0 + 20}}{2}} \right) \times 0.5 \\
\Rightarrow s = 10 \times 0.5 \\
\therefore s = 5m \\
$
Hence, the required solution is - the distance travelled after by the car will be $5m$.

Note: Remember the basic three equations of motion to find the components such as the displacement, the initial and the final velocity, acceleration and time. The term displacement and the distance both are the same. Know the representative units of all terms. To be noted that the velocity of any object at rest or at stationary is always zero.