Question

A train starting from rest attains a velocity of 20m/s in 2 minutes. Assuming that the acceleration is uniform, find-
A. Acceleration
B. Distance travelled by the train while it attained its velocity

Answer 1

Hint: We will apply the first equation of motion in order to get the answer of the first part of the question. Then we will apply the third equation of motion in order to find the distance travelled by the train. Refer to the solution below.

Formula used: $v = u + at$, ${v^2} = {u^2} + 2as$

Complete Step-by-Step solution:
a) Since the train is starting from rest so its initial velocity will be $u = 0$.
Final velocity of the train is given in the question i.e. $v = 20m/s$
Time given in the question is 2 minutes = 120 seconds.
So, applying the first equation of motion i.e. $v = u + at$ , we will find out the value of acceleration.
Putting the values in the above equation, we will get-
$
   \Rightarrow v = u + at \\
    \\
   \Rightarrow 20 = 0 + a \times 120 \\
    \\
   \Rightarrow a = \dfrac{1}{6}m/{s^2} \\
$

b) Since the train is starting from rest so its initial velocity will be $u = 0$.
Final velocity of the train is given in the question i.e. $v = 20m/s$
Time given in the question is 2 minutes = 120 seconds.
Now, we will apply the third equation of motion i.e. ${v^2} = {u^2} + 2as$, where s is the distance.
Putting all the values in the above formula, we will get-
$
   \Rightarrow {v^2} = {u^2} + 2as \\
    \\
   \Rightarrow {20^2} = 0 + 2 \times \dfrac{1}{6} \times s \\
    \\
   \Rightarrow 400 = 0 + \dfrac{1}{3} \times s \\
    \\
   \Rightarrow s = 1200m \\
$

Note: Motion equations are equations which describe the physical system's behavior in terms of its motion as a function of time. More precisely, motion equations describe the physical system's behavior as a collection of mathematical functions in terms of dynamic variables.