Question

A train starts to move from rest.It is accelerated by 4 m/s².Calculate its velocity and time needed to travel 50 m distance.

Answer 1

★ Given :

• Initial velocity of train (u) = 0m/s
• Acceleration of train (a) = 4 m/s²
• Distance travelled by train (s) = 50 m

★ To Find :

We have to find the final velocity and time taken by the train.

★ Explanation :

As, we have to find the time taken. So, firstly we will use second equation of the motion.

$\large{\star{\underline{\boxed{\sf{s = ut + \dfrac{1}{2} at^2}}}}}$

$\rm{\dashrightarrow 50 = 0(t) + \dfrac{1}{\cancel{2}} \times \cancel{4} \times t^2} \\ \\ \rm{\dashrightarrow 50 = 0 + 2t^2} \\ \\ \rm{\dashrightarrow t^2 = \dfrac{\cancel{50}}{\cancel{2}}} \\ \\ \rm{\dashrightarrow t^2 = 25} \\ \\ \rm{\dashrightarrow t = \sqrt{25}} \\ \\ \rm{\dashrightarrow t = \pm 5}$

As, time taken can't be negative. So, t = 5s

$\large{\star{\underline{\boxed{\sf{t = 5 \: s}}}}}$

$\rule{200}{2}$

Now,

We will use first equation of motion to find the final velocity.

$\large{\star{\underline{\boxed{\sf{v = u + at}}}}}$

$\rm{\dashrightarrow v = 0 + 4(5)} \\ \\ \rm{\dashrightarrow v = 20}$

$\large{\star{\underline{\boxed{\sf{v = 20 \: ms^{-1}}}}}}$

$\rule{400}{4}$

Answer 2

Given :

• Initial velocity (u) = 0 m/s
• Acceleration (a) = 4 m/s²
• Distance Travelled (s) = 50 m

To Find :

• Velocity and time needed to travel 50 m

Solution :

We are given that the car starts from rest. So, initial velocity (u) will be taken as 0 m/s. We've to find out velocity and time when the distance travelled is 50 m

Use 3rd equation of motion :

$\implies \sf{v^2 \: - \: u^2 \: = \: 2as} \\ \\ \implies \sf{v^2 \: - \: 0^2 \: = \: 2 \: \times \: 4 \: \times \: 50} \\ \\ \implies \sf{v^2 \: = \: 8 \: \times \: 40} \\ \\ \implies \sf{v^2 \: = \: 400} \\ \\ \implies \sf{v \: = \: \sqrt{400}} \\ \\ \implies \sf{v \: = \: \pm 20}$

As we know that velocity can't be taken as negative. So, we will take positive velocity.

$\therefore$ Velocity when car travels 50m is 20 m/s

______________________________

Now, use 1st equation of motion :

$\implies \sf{v \: = \: u \: + \: at} \\ \\ \implies \sf{20 \: - \: 0 \: = \: 4t} \\ \\ \implies \sf{4t \: = \: 20} \\ \\ \implies \sf{t \: = \: \dfrac{20}{4}} \\ \\ \implies \sf{t \: = \: 5}$

$\therefore$ Time when car travels 50m is 5 seconds.