Question

A train is travelling at a speed of 90 km/hr. Brakes are applied so as to produce a uniform acceleration of -0.5 m/$s_2$. Find how far the train will go before it is brought to rest?
A. 625 m
B. 4050 m
C. 8100 m
D. 1250 m

Answer 1

Hint: Before attempting this question one should have prior knowledge of equations of motion and remember to take final velocity as 0 km/hr, use this information to approach towards the solution of the problem.

Complete step by step answer:
According to the given information train is travelling at a speed of 90 km/hr so initial speed of train is 90 km/hr when brakes are applied which produces acceleration of -0.5 m/$s_2$ i.e. a = -0.5 m/$s_2$
So since the brakes are applied to stop the train it means the final velocity of the train will be 0 i.e. v = 0 km/hr
We have u = 90 km/hr = $90 \times \dfrac{5}{{18}}$ = 25 m/s
To find the distance travelled by the train let’s use the 3rd equation of motion i.e. \[{v^2} - {u^2} = 2aS\]
Substituting the given values in the 3rd equation of motion we get
\[{0^2} - {\left( {25} \right)^2} = 2 \times \left( { - 0.5} \right) \times S\]
$ \Rightarrow $- \[625 = - 1 \times S\]
$ \Rightarrow $\[S = \dfrac{{ - 625}}{{ - 1}}\]
S = 625 m
So the total distance travelled by the train is 625 m
Hence, the correct answer is option A.

Note:
In the above question we came across the term acceleration which can be explained as the rate of change in velocity of an object, acceleration is of 2 types one is uniform acceleration which means the constant change in rate of velocity in equal interval of time of an object and another is non-uniform acceleration which means the variable change in rate of change in velocity in equal interval of time of an object. Let’s take help of an example to explain this topic suppose you and your friend have car and you both started the car from the same point to some finite distance you are driving the car with same change in rate of velocity in equal interval to time whereas your friend is driving with non-equal change in rate of velocity in equal interval of time so in this case you are driving the car with some uniform acceleration which is the constant change in rate of velocity of your car in equal interval of time but your friend is driving the car with some non-uniform acceleration which is the non-constant change in the rate of velocity of your car in equal interval of time.