Question

A train traveling at 20 m/s accelerates for 1 m/s sq for 30 secs how far will it travel in this time?

Answer 1

Answer:

Given:

Train travelling at 20 m/s .

Acceleration = 1 m/s²

Time = 30 secs.

To find:

Distance travelled in this time interval.

Concept:

Acceleration is a vector Quantity which indicates the rate of change of velocity over time.

$\boxed{acc. = \dfrac{\Delta v}{\Delta t} }$

Calculation:

The relationship between Acceleration , distance and time can be given as follows;

$s = ut \: + \frac{1}{2} a {t}^{2}$

$= > s = (20 \times 30) + \{ \frac{1}{2} \times 1 \times {(30)}^{2} \}$

$= > s = 600 + 450$

$= > s = 1050 \: m$

So final answer is :

$\boxed{\huge{\red{\bold{\underline{ s = 1050 \: m}}}}}$

Additional information :

• Distance is the total path length traversed by a body
• It is always positive
• It can be never be zero or negative.
• It's a scalar Quantity having only magnitude.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Train\:travelled\:in\:30\:sec=1.05\:km}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Initial \: speed(u) = 20 \: m/s \\ \\ \tt: \implies Acceleration(a) = 1 \: m/s^{2} \\ \\ \tt: \implies Time(t) = 30 \: sec \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Distance \: travelled(s) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies s = ut + \frac{1}{2} a {t}^{2} \\ \\ \text{Putting \: given \: value} \\ \tt: \implies s = 20 \times 30 + \frac{1}{2} \times 1 \times {30}^{2} \\ \\ \tt: \implies s =600 + \frac{1}{2} \times 900 \\ \\ \tt: \implies s =600 + 450 \\ \\ \green{\tt: \implies s =1050 \: m} \\ \\ \tt\green{\therefore Train \: travelled \: \: 1.05 \: km \: in \: 30 \: sec} \\ \\ \blue{\bold{Some \: formula \: realted \: to \: this \: topic}} \\ \orange{\tt \circ \: v = u + at }\\ \\ \orange{\tt \circ \: {v}^{2} = {u}^{2} + 2as}$