Question

A car of mass $1000\,kg$ moving with a velocity of $40\,km{h^{ - 1}}$ collides with a tree and comes to a stop in $5\,s$ What will be the force exerted by the car on the tree?
A. $2222.22\,N$
B. $1111.11\,N$
C. $3333.33\,N$
D. None of these

Answer 1

In order to solve this question, we should know that when a body came to rest its final velocity became zero and here, we will use the general formula of finding the acceleration of the car and then by using formula of force, we will calculate magnitude of force exerted by car on tree.

Formula used:
If $u, v$ are the initial, final velocity of a body in time $t$ then, acceleration is calculated as $a = \dfrac{{v - u}}{t}$
If $m, a$ be the mass and acceleration of moving body, then force $F$ is written as
$F = ma$

Complete step by step answer:
According to the question, we have before hitting the tree car has the initial velocity of $u = 40\,km{h^{ - 1}} = \dfrac{{40 \times 5}}{{18}}\,m{s^{ - 1}}$ since $(1\,km{h^{ - 1}} = \dfrac{5}{{18}}\,m{s^{ - 1}})$ and when it hit the tree and came to rest after a time of $t = 5\sec$ its final velocity became $v = 0$.

So, acceleration produced in between this by the car is, using $a = \dfrac{{v - u}}{t}$ we get,
$a = \dfrac{{0 - (\dfrac{{40 \times 5}}{{18}})}}{5}$
$\Rightarrow a = - \dfrac{{40}}{{18}}\,m{s^{ - 2}}$
Now, we have mass of the car is $m = 1000kg$ and acceleration is $a = - \dfrac{{40}}{{18}}\,m{s^{ - 2}}$ so force exerted by car on tree is,
$F = ma$
We get,
$\Rightarrow F = - (1000 \times \dfrac{{40}}{{18}})$
$\therefore F = - 2222.22\,N$
Since, negative sign implies that, force is retarding force as body comes to rest.

Hence, the correct option is A.

Note: It should be remembered that, negative acceleration simple means body has reduced its velocity from initial condition and hence force acting on it is retarding force and here force exerted by tree on car and force exerted by car on tree are both equal in magnitude but opposite in directions.